TS EAMCET · Maths · Trigonometric Ratios & Identities
For some \(a, b, c \in \mathbf{R}\), if \(\sin 5 \theta=a \cos ^4 \theta \sin \theta+b \cos ^2 \theta \sin ^3 \theta+c \sin ^5 \theta\), then \(a b c=\)
- A -10
- B 10
- C 0
- D -50
Answer & Solution
Correct Answer
(D) -50
Step-by-step Solution
Detailed explanation
Given, \(\sin 5 \theta=a \cos ^4 \theta \sin \theta+b \cos ^2 \theta \sin ^3 \theta+c \sin ^5 \theta\) at \(\theta=\frac{\pi}{2}\), we get \(1=0+0+c \Rightarrow c=1\) \(\ldots(\mathrm{i})\) at \(\quad \theta=\frac{\pi}{4}\), we get…
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