R.S. Aggarwal solutions for Mathematics [English] Class 10 chapter 5 - Trigonometric Ratios [Latest edition]

If sin θ ,` sqrt (3)/2` find the value of all T- ratios of θ .

If cos θ  = `7/25` find the value of all T-ratios of  θ   .

If tan θ =`15/ 8 `, find the values of all T-ratios of θ.

If cot θ =  2 find all the values of all T-ratios of θ .

If cosec θ = `sqrt(10)` find all the values of all T-ratios of θ

If sin θ = ` (a^2 - b^2)/(a^2+b^2)`find all the values of all T-ratios of θ .

Given 15 cot A = 8. Find sin A and sec A.

If sin A = `9/41` find all the values of cos A and tan A

If cos θ=0.6 show that (5sin θ -3tan θ) = 0

If cosec θ= 2 show that `(cot θ +sin θ /(1+cos θ )) =2`

If `tan θ = 1/sqrt(7)`, show that `("cosec"^2θ - sec^2θ)/("cosec"^2θ + sec^2θ) = 3/4` .

If tan θ = `20/21` show that `((1-sin θ + cos θ))/((1+ sin θ +cos θ)) = 3/7`

If sec θ = `5/4 ` show that `((sin θ   - 2 cos θ))/(( tan θ - cot θ)) = 12/7`

If  cot  θ = `3/4` , show that `sqrt("sec θ - cosecθ"/"secθ + cosecθ" ) = 1/ sqrt(7)`

If sin θ = `3/4` show that `sqrt((cosec^2theta - cot^2theta)/(sec^2theta-1)) =sqrt(7)/3` 

If sin θ = `a/b`, show that `(sectheta + tan theta) = sqrt((b+a)/(b-a))`

If cos θ = `3/5` , show that `((sin theta - cot theta ))/(2tan theta)=3/160`

If tan θ = `4/3`, show that `(sintheta + cos theta )=7/5`

If tan `theta = a/b`, show that `((a sin theta - b cos theta))/((a sin theta + bcos theta))= ((a^2-b^2))/(a^2+b^2)`

If 3tan θ   4 , show that `((4cos theta - sin theta ))/((4 cos theta + sin theta))=4/5`

If 3 cot `theta = 2, `show  that `((4 sin theta - 4 cos theta))/((2 sin theta + 6 cos theta ))=1/3`

If 3 cot θ 4 , show that`((1-tan^2theta))/((1+tan^2theta)) = (cos^2theta - sin^2theta)`

If sec `theta = 17/8 ` verify that `((3-4sin^2theta)/(4 cos^2theta -3))=((3-tan^2theta)/(1-tan^2theta))`

In the adjoining figure, `∠B  = 90° , ∠BAC = theta° , BC = CD = 4cm and AD = 10 cm`. find  (i)  sin theta and (ii) `costheta`

In a ΔABC , ∠B = 90° , AB= 24 cm and BC = 7 cm find (i) sin A (ii) cos A (iii) sin C (iv) cos C

In ΔABC , ∠C = 90°  ∠ABC = θ°   BC = 21 units . and AB= 29 units. Show thaT `(cos^2 theta - sin^2 theta)=41/841`

In a ΔABC , ∠B = 90° , AB = 12 cm and BC = 5 cm Find
(i) cos A (ii) cosec A (iii) cos C (iv) cosec C

If sin ∝  = `1/2` prove that (3cos∝ - `4cos^2` ∝)=0

In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of

1.  sin A cos C + cos A sin C
2. cos A cos C − sin A sin C

If ∠A and ∠B are acute angles such that sin A = Sin B prove that ∠A = ∠B.

If ∠A and ∠B are acute angles such that tan A= Tan B then prove that ∠A = ∠B

If a right ΔABC , right-angled at B, if tan A=1 then verify that 2sin A . cos A = 1

In the figure of ΔPQR , ∠P = θ°  and ∠R =∅° find
(i)  `sqrt(X +1) cot ∅`

(ii)`sqrt( x^3 + x ^2) tantheta`

(iii) cos θ 

If x = cosec A +cos A and y = cosec A – cos A then prove that `(2/(x+y))^2 + ((x-y)/2)^2` = 1

If x = cot A + cos A and y = cot A – cos A then prove that `((x-y)/(x+y))^2 + ((x-y)/2)^2=1`