Question

I need answer quickly

Answer 1

Answer:

2) Sinx = tan² ( α / 2 )

Step-by-step explanation:

Given---->

Cot⁻¹ ( √Cosα ) - tan⁻¹ ( √Cosα ) = x

To find ----> Value of Sinx

Solution----->

1) Plzzz see the attachment

2) First , we take given relation

3) Now , we know that,

Cot⁻¹ ( x ) = tan⁻¹ ( 1 / x ) , applying it

4) Now , we know that,

tan⁻¹ ( x ) - tan⁻¹ ( y ) = tan⁻¹ ( x - y ) / ( 1 + xy ) , applying it and solving it we get,

tanx = ( 1 - Cosα ) / 2 √Cosα

5) Now , we use it to find value of Sinθ by applying PGT , and get,

Sinx = ( 1 - Cosα ) / ( 1 + Cosα )

6) Now , we know that ,

Cosθ = 2 Cos²θ/2 - 1 = 1 - 2Sin²θ/2

Applying these formulee we get the answer.