TS EAMCET · Maths · Trigonometric Equations
If \(\sin 6 \theta=32 \cos ^5 \theta \sin \theta-32 \cos ^3 \theta \sin \theta+3 x\) then \(x\) is equal to :
- A \(\cos \theta\)
- B \(\cos 2 \theta\)
- C \(\sin \theta\)
- D \(\sin 2 \theta\)
Answer & Solution
Correct Answer
(D) \(\sin 2 \theta\)
Step-by-step Solution
Detailed explanation
We have, \(\sin 6 \theta=\sin 3(2 \theta)\) \(=3 \sin 2 \theta-4 \sin ^3 2 \theta\) \(=3 \cdot 2 \sin \theta \cos \theta-4 \cdot 8 \cdot \cos ^3 \theta \sin ^3 \theta\) \(=6 \sin \theta \cos \theta-32 \cos ^3 \theta \sin \theta\left(1-\cos ^2 \theta\right)\)…
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