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R.S. Aggarwal solutions for Class 10 Mathematics chapter 8 - Trigonometric Identities

Secondary School Mathematics for Class 10 (for 2019 Examination)

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R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

Secondary School Mathematics for Class 10 (for 2019 Examination) - Shaalaa.com

Chapter 8: Trigonometric Identities

Chapter 8: Trigonometric Identities solutions [Page 0]

(i)` (1-cos^2 theta )cosec^2theta = 1`

`(1 + cot^2 theta ) sin^2 theta =1`

`(sec^2 theta-1) cot ^2 theta=1`

`(sec^2 theta -1)(cosec^2 theta - 1)=1`

`(1-cos^2theta) sec^2 theta = tan^2 theta`

`sin^2 theta + 1/((1+tan^2 theta))=1`

`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`

`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`

`cosec theta (1+costheta)(cosectheta - cot theta )=1`

`cot^2 theta - 1/(sin^2 theta ) = -1`a

` tan^2 theta - 1/( cos^2 theta )=-1`

`cos^2 theta + 1/((1+ cot^2 theta )) =1`

     

`1/((1+ sintheta ))+1/((1- sin theta ))= 2 sec^2 theta`

`sec theta (1- sin theta )( sec theta + tan theta )=1`

`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec  theta)`

`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`

`1+(tan^2 theta)/((1+ sec theta))= sec theta`

`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`

`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`

`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`

`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec  theta)`

`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`

`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`

`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`

`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`

`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`

`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`

`cosec ^4 theta + cosec^2 theta = cot^4 theta+ cot^2 theta`

`(1+ tan^2 theta)/(1+ tan^2 theta)= (cos^2 theta - sin^2 theta)`

`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`

`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`

`cot theta/((cosec  theta + 1) )+ ((cosec  theta +1 ))/ cot theta = 2 sec theta `

`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`

`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`

`sqrt((1+sin theta)/(1-sin theta)) = (sec theta + tan theta)`

`sqrt((1-cos theta)/(1+cos theta)) = (cosec  theta - cot  theta)`

`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`

 

`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`

`sin theta/((cot theta + cosec  theta)) - sin theta /( (cot theta - cosec  theta)) =2`

` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`

` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`

`(1+ cos  theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`

`(cos  ec^theta + cot theta )/( cos ec theta - cot theta  ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta  cot theta`

`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `

`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`

`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`

`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`

`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`

`(cos theta  cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`

`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`

`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`

`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`

`((sin A-  sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0` 

`(tan A + tanB )/(cot A + cot B) = tan A tan B`

Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`

Show that none of the following is an identity: 

`sin^2 theta + sin  theta =2`

Show that none of the following is an identity:

`tan^2 theta + sin theta = cos^2 theta`

Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`

Chapter 8: Trigonometric Identities solutions [Page 0]

If a cos `theta + b sin theta = m and a sin theta - b cos theta = n , "prove that "( m^2 + n^2 ) = ( a^2 + b^2 )`

If x= a sec `theta + b tan theta and y = a tan theta + b sec theta ,"prove that" (x^2 - y^2 )=(a^2 -b^2)`

If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`

If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1

If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.

If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`

If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`

If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`

If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`

If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`

If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.

If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`

If `sec theta + tan theta = p,` prove that

(i)`sec theta = 1/2 ( p+1/p)   (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`

If tan A = n tan B and sin A = m sin B , prove that  `cos^2 A = ((m^2-1))/((n^2 - 1))`

If m = ` ( cos theta - sin theta ) and n = ( cos theta +  sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.

Chapter 8: Trigonometric Identities solutions [Page 0]

Write the value of `( 1- sin ^2 theta  ) sec^2 theta.`

Write the value of `(1 - cos^2 theta ) cosec^2 theta`.

Write the value of `(1 + tan^2 theta ) cos^2 theta`. 

Write the value of `(1 + cot^2 theta ) sin^2 theta`. 

Write the value of `(sin^2 theta 1/(1+tan^2 theta))`. 

Write the value of `(cot^2 theta -  1/(sin^2 theta))`. 

Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`. 

Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`

 

Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`

Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`

Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`

Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`

Write the value of `3 cot^2 theta - 3 cosec^2 theta.`

Write the value of `4 tan^2 theta  - 4/ cos^2 theta`

Write the value of`(tan^2 theta  - sec^2 theta)/(cot^2 theta - cosec^2 theta)`

If  `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`

If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`

If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`

If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`

If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`

If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`

If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`

If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`

If ` cot A= 4/3 and (A+ B) = 90°  `  ,what is the value of tan B?

If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.

If `sqrt(3) sin theta = cos theta  and theta ` is an acute angle, find the value of θ .

Write the value of tan10° tan 20° tan 70° tan 80° .

Write the value of tan1° tan 2°   ........ tan 89° .

Write the value of cos1° cos 2°........cos180° .

If tan A =` 5/12` ,  find the value of (sin A+ cos A) sec A.

`If sin theta = cos( theta - 45° ),where   theta   " is   acute, find the value of "theta` .

Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50°   cosec 40 °`

Find the value of sin ` 48° sec 42° + cos 48°  cosec 42°`

 

If x =  a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`

If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`

If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`

If `sec theta + tan theta = x,"  find the value of " sec theta`

Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`

If `sin theta = x , " write the value of cot "theta .`

If `sec theta = x ,"write the value of tan"  theta`.

Chapter 8: Trigonometric Identities

R.S. Aggarwal Secondary School Mathematics Class 10 (for 2019 Examination)

Secondary School Mathematics for Class 10 (for 2019 Examination) - Shaalaa.com

R.S. Aggarwal solutions for Class 10 Mathematics chapter 8 - Trigonometric Identities

R.S. Aggarwal solutions for Class 10 Maths chapter 8 (Trigonometric Identities) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Secondary School Mathematics for Class 10 (for 2019 Examination) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. R.S. Aggarwal textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 8 Trigonometric Identities are Trigonometric Ratios of Complementary Angles, Trigonometric Identities.

Using R.S. Aggarwal Class 10 solutions Trigonometric Identities exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in R.S. Aggarwal Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer R.S. Aggarwal Textbook Solutions to score more in exam.

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