Verify Each of the Following: (Iv) `2 Sin 45^0 Cos 45^0` - Mathematics

Advertisements
Advertisements

Verify each of the following:

(iv) `2 sin 45^0 cos 45^0` 

Advertisements

Solution

`2  sin  45^0   cos  45^0` 

=`2xx1/sqrt(2) xx1/sqrt(2) =1`

Also, sin `90^0 =1`

∴ `2  sin 45^0  cos 45^0 = sin 90^0` 

  Is there an error in this question or solution?
Chapter 6: T-Ratios of some particular angles - Exercises

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 6 T-Ratios of some particular angles
Exercises | Q 11.4

RELATED QUESTIONS

If 𝜃 = 30° verify `cos 2 theta = (1 - tan^2 theta)/(1 + tan^2 theta)`


In rectangle ABCD AB = 20cm ∠BAC = 60° BC, calculate side BC and diagonals AC and BD.


In ∆PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠P and ∠R.


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


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


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


Verify each of the following:

(i)`sin 60^0 cos 30^0-cos 60^0 sin 30^0`


Verify each of the following:

(iii) `2 sin 30^0 cos 30^0`


Using the formula, cos A = `sqrt((1+cos2A)/2) ,`find the value of cos 300, it being given that cos 600  = `1/2`.


Using the formula, sin A = `sqrt((1-cos 2A)/2) ` find the value of sin 300, it being given that cos 600 = `1/2` 


In the following table, a ratio is given in each column. Find the remaining two ratios in the column and complete the table.

sin θ    `11/61`   `1/2`       `3/5`  
cos θ `35/37`       `1/sqrt3`        
tan θ     `1`     `21/20` `8/15`   `1/(2sqrt2)`

`(cos 28°)/(sin 62°)` = ?


sin20°   =  cos ______°


tan 30° × tan ______°  = 1


cos 40° = sin ______°


From the following figure, find the values of :

  1. sin A
  2. cos A
  3. cot A
  4. sec C
  5. cosec C
  6. tan C.


Given: 4 cot A = 3
find :

(i) sin A
(ii) sec A
(iii) cosec2A - cot2A.


If cot θ= 1; find the value of: 5 tan2 θ+ 2 sin2 θ- 3


In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find:
(i) sin B 
(ii) tan C
(iii) sin2 B + cos2
(iv) tan C - cot B


In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find:

  1. cos B
  2. sin C
  3. tan2 B - sec2 B + 2

If sin A = `(sqrt3)/(2)` and cos B = `(sqrt3)/(2)` , find the value of : `(tan"A" – tan"B")/(1+tan"A" tan"B")`


In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.

sec B = `(15)/(12)`


In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: cos C


If sinA = 0.8, find the other trigonometric ratios for A.


In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: cot2P - cosec2P


From the given figure, find all the trigonometric ratios of angle B


From the given figure, find the values of cot B


From the given figure, find the values of cosec C


If cos A = `3/5`, then find the value of `(sin"A" - cos"A")/(2tan"A")`


If cos A = `(2x)/(1 + x^2)`, then find the values of sin A and tan A in terms of x


If 3 cot A = 2, then find the value of `(4sin"A" - 3cos"A")/(2sin"A" + 3cos"A")`


If cos θ : sin θ = 1 : 2, then find the value of `(8costheta - 2sintheta)/(4costheta + 2sintheta`


From the given figure, prove that θ + ∅ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ∅


A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)


Given that sin α = `1/2` and cos β = `1/2`, then the value of α + β is ______.


Share
Notifications



      Forgot password?
Use app×