Question

Let y = cos^–1[(2 cos x + 3 sin x)/$\sqrt{13}$]. Then $\frac{dy}{dx}$= 1 –

• A. For all x
• B. For tan^–1 3/2 < x <π + tan^–13/2
• C. For – {π – tan^–1 (3/2) < x < tan^–1(3/2)}
• D. For no x.

Answer 1

Answer: (A)

For all x

Answer 2

cos^–1$\left\lbrack \frac{2}{\sqrt{13}}\cos x + \frac{3}{\sqrt{13}}\sin x \right\rbrack$

↓               ↓

cos α sin α      

tan α = 3/2

α = tan^–13/2

y = cos^–1[cos (x − α)]

⇒  y = x − α  

$\frac{dy}{dx}$ = 1 (Q 0 < x – α < π)

⇒ α < x < α + π