Prove that 3 sin frac{π}{6} sec frac{π}{3}-4 sin frac{5 π}{6} cot frac{π}{4}=1

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3.Trigonometrical Ratios, Functions and Identities

easy

Prove that

$3 \sin \frac{\pi}{6} \sec \frac{\pi}{3}-4 \sin \frac{5 \pi}{6} \cot \frac{\pi}{4}=1$

Option A

Option B

Option C

Option D

Solution We have

${\text{ L}}{\text{.H}}{\text{.S}}{\text{.}} = 3\sin \frac{\pi }{6}\sec \frac{\pi }{3} – 4\sin \frac{{5\pi }}{6}\cot \frac{\pi }{4}$

$ = 3 \times \frac{1}{2} \times 2 – 4\sin \left( {\pi – \frac{\pi }{6}} \right) \times 1 = 3 – 4\sin \frac{\pi }{6}$

$ = 3 – 4 \times \frac{1}{2} = 1 = R.H.S$

Standard 11

Mathematics

easy

medium

(IIT-1970)

easy

easy

easy