AP EAMCET · Maths · Differentiation
If \(3 f(\cos x)+2 f(\sin x)=5 x\), then \(f^{\prime}(\cos x)+f^{\prime}(\sin x)=\)
- A \(-5(\sin x+\cos x)\)
- B \(-5 \sin x \cos x\)
- C \(\frac{-5}{\sin x}-\frac{5}{\cos x}\)
- D \(\frac{5}{\sin x}+\frac{5}{\cos x}\)
Answer & Solution
Correct Answer
(C) \(\frac{-5}{\sin x}-\frac{5}{\cos x}\)
Step-by-step Solution
Detailed explanation
\(3 f(\cos x)+2 f(\sin x)=5 x\) ...(i) \(3 f(\sin x)+2 f(\cos x)=5\left(\frac{\pi}{2}-x\right)\) ...(ii) Solving Eqs. (i) and (ii) simultaneously, we get \(f(\cos x)=5 x-\pi\)…
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