JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y =\sum \limits_{ k =1}^{6} k \cos ^{-1}\left\{\frac{3}{5} \cos k x -\frac{4}{5} \sin k x \right\}\) then \(\frac{ dy }{ dx }\) at \(x =0\) is
- A \(90\)
- B \(91\)
- C \(88\)
- D \(89\)
Answer & Solution
Correct Answer
(B) \(91\)
Step-by-step Solution
Detailed explanation
Put \(\cos \alpha=\frac{3}{5}, \sin \alpha=\frac{4}{5} \quad 0<\alpha<\frac{\pi}{2}\) Now \(\frac{3}{5} \cos kx -\frac{4}{5} \sin kx\) \(=\cos \alpha \cdot \cos kx -\sin \alpha \cdot \sin kx\) \(=\cos (\alpha+k x)\) As we have to find derivate at \(x=0\) We have…
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