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3.Trigonometrical Ratios, Functions and Identities
medium
Prove that $2 \sin ^{2}\, \frac{3 \pi}{4}+2 \cos ^{2}\, \frac{\pi}{4}+2 \sec ^{2}\, \frac{\pi}{3}=10$
Option A
Option B
Option C
Option D
Solution
$L.H.S.$ $=2 \sin ^{2} \,\frac{3 \pi}{4}+2 \cos ^{2}\, \frac{\pi}{4}+2 \sec ^{2}\, \frac{\pi}{3}$
$=2\left\{\sin \left(\pi-\frac{\pi}{4}\right)\right\}^{2}+2\left(\frac{1}{\sqrt{2}}\right)^{2}+2(2)^{2}$
$=2\left\{\sin \frac{\pi}{4}\right\}^{2}+2 \times \frac{1}{2}+8$
$=1+1+8$
$=10$
$= R . H.S$
Std 11
Mathematics
