If y = tan^-1((sin x + cos x)/(cos x - sin x)), then dy/dx is equal to A. 1/2 B. 0 C. 1 D. none of these

Question

If y = tan^-1\(\Big(\cfrac{sin\,\text x+cos\,\text x}{cos\,\text x-sin\,\text x}\Big),\) then \(\cfrac{dy}{d\mathrm x} \) is equal to

A. \(\cfrac{1}{2}\)

B. 0

C. 1

D. none of these

Answer 1

Correct option is C. 1

y = tan^-1\(\Big(\cfrac{sin\,\text x+cos\,\text x}{cos\,\text x-sin\,\text x}\Big)\)

Dividing Numerator and denominator by cos x we get,

Differentiating w.r.t x we get

\(\cfrac{dy}{d\mathrm x} \) = 1