​ If y = tan^-1 {cos x+sin x/cos x - sin x} then dy/dx = ? ​A. 1 B. -1 C. 1/2 D.-1/2

Question

If y = tan^-1 \(\left\{\frac{cosx+sinx}{cosx-sinx}\right\}\) then dy/dx = ?

{cos x+sin x/cos x - sin x}

A. 1

B. -1

C. 1/2

D.-1/2

Answer 1

Answer is: A. 1

Given that y = tan^-1 \(\left\{\frac{cosx+sinx}{cosx-sinx}\right\}\)

Dividing numerator and denominator with cosx, we get

Differentiating with respect to x, we get

dy/dx = 1