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

If $\sin \theta = \frac{{ - 4}}{5}$ and $\theta $ lies in the third quadrant, then $\cos \frac{\theta }{2} = $

Prove that $\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)=-\sqrt{2} \sin x$

Let the function $:(0, \pi) \rightarrow R$ be defined by

$f (\theta)=(\sin \theta+\cos \theta)^2+(\sin \theta-\cos \theta)^4$

Suppose the function $f$ has a local minimum at $\theta$ precisely when $\theta \in\left\{\lambda_1 \pi, \ldots, \lambda_{ T } \pi\right\}$, where $0<\lambda_1<\cdots<\lambda_r<1$. Then the value of $\lambda_1+\cdots+\lambda_r$ is. . . . . 

  • [IIT 2020]

If $\tan \theta - \cot \theta = a$ and $\sin \theta + \cos \theta = b,$ then ${({b^2} - 1)^2}({a^2} + 4)$ is equal to

Find the value of the trigonometric function $\cos ec \left(-1410^{\circ}\right)$