AP EAMCET · Maths · Differentiation
If \(f(x)=\sin x \cdot \sin 2 x \cdot \sin 3 x\) and \(f^{\prime \prime}(x)=a(\sin b x)+c(\sin d x)+e(\sin k x)\), then the value of \((a+c+e)-(b+d+k)\) equals
- A 8
- B -8
- C 16
- D 12
Answer & Solution
Correct Answer
(D) 12
Step-by-step Solution
Detailed explanation
\text { } \begin{aligned} f(x) & =\sin x \sin 2 x \cdot \sin 3 x \\ & =\frac{(2 \sin x \sin 2 x) \sin 3 x}{2} \\ & =\frac{1}{2}\{\cos x-\cos 3 x\} \sin 3 x \\ & =\frac{1}{2}[\cos x \sin 3 x-\cos 3 x \sin 3 x] \\ & =\frac{2}{4} \cos x \sin 3 x-\frac{2}{4} \cos 3 x \sin 3 x \\ &…
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