Question

`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______ 

विकल्प

• 0

• 1

• `sqrt2`

• `1/sqrt2`

Answer 1

`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to 1.

Explanation:

Putting x = tan θ, we get

`sin[tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))]` 

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

= `sin[tan^1(cot2theta) + cos^-1 (cos2theta)]`

= `sin[tan^-1{tan(pi/2 - 2theta)} + cos^-1(cos2theta)]`

= `sin  pi/2`

= 1