JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(\sin \theta+\cos \theta=\frac{1}{2}\), then \(16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))\) is equal to:
- A \(27\)
- B \(-27\)
- C \(-23\)
- D \(23\)
Answer & Solution
Correct Answer
(C) \(-23\)
Step-by-step Solution
Detailed explanation
\(16[2 \sin 4 \theta \cos 2 \theta+\cos 4 \theta]\) \(16\left[4 \sin 2 \theta \cos ^{2} 2 \theta+2 \cos ^{2} 2 \theta-1\right]\) Now: \(\sin \theta+\cos \theta=\frac{1}{2}\) \(1+\sin 2 \theta=\frac{1}{4}\) \(\sin 2 \theta=-\frac{3}{4}\)…
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