MHT CET · Maths · Trigonometric Ratios & Identities
\(\sin \left(\frac{\pi}{3}+x\right)-\cos \left(\frac{\pi}{6}+x\right)=\)
- A \(-\cos x\)
- B \(-\sin x\)
- C \(\cos x\)
- D \(\sin x\)
Answer & Solution
Correct Answer
(D) \(\sin x\)
Step-by-step Solution
Detailed explanation
\(\sin \left(\frac{\pi}{3}+x\right)-\cos \left(\frac{\pi}{6}+x\right)\)
\(=\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x-\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x\)
\(=\sin x\)
\(=\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x-\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x\)
\(=\sin x\)
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