Question

If y = cos^–1$\left( \frac{3\cos x + 5\sin x}{\sqrt{34}} \right)$, then $\frac{dy}{dx}$ is –

• A. 0
• B. – 1
• C. 1
• D. None of these

Answer 1

let y = cos^–1$\left\lbrack \frac{3}{\sqrt{34}}\cos x + \frac{5}{\sqrt{34}}\cos x \right\rbrack\left| {}_{5 = r\cos\theta}^{3 = r\sin\theta} \right.\$

r = $\sqrt{34}$ & q = tan^–1$\frac{3}{5}$

y = cos^–1[sinq.cosx + cosq.sinx]

= cos^–1[sin(x+q)] = cos^–1$\left( \cos{}\left( \frac{x}{2} - x - \theta \right) \right)$

y = $\frac{\pi}{2}$– x – q = $\frac{\pi}{2}$– x – tan^–1$\frac{3}{5}$

\frac{dy}{dx} = - 1 \end{matrix}$$