Prove that $2 \sin ^{2}\, \frac{3 \pi}{4}+2 \cos ^{2}\, \frac{\pi}{4}+2 \sec ^{2}\, \frac{\pi}{3}=10$

Vedclass pdf generator app on play store
Vedclass iOS app on app store

$L.H.S.$ $=2 \sin ^{2} \,\frac{3 \pi}{4}+2 \cos ^{2}\, \frac{\pi}{4}+2 \sec ^{2}\, \frac{\pi}{3}$

$=2\left\{\sin \left(\pi-\frac{\pi}{4}\right)\right\}^{2}+2\left(\frac{1}{\sqrt{2}}\right)^{2}+2(2)^{2}$

$=2\left\{\sin \frac{\pi}{4}\right\}^{2}+2 \times \frac{1}{2}+8$

$=1+1+8$

$=10$

$= R . H.S$

Similar Questions

Which of the following relations is correct

Find the value of $\tan \frac{13 \pi}{12}$

The equation ${(a + b)^2} = 4ab\,{\sin ^2}\theta $ is possible only when

If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre, find the ratio of their radii.

Find $\sin \frac{x}{2}, \cos \frac{x}{2}$ and $\tan \frac{x}{2}$ for $\sin x=\frac{1}{4}, x$ in quadrant $II$