The real roots of the equation $cos^7x\, +\, sin^4x\, =\, 1$ in the interval $(-\pi, \pi)$ are
$ \{- \frac{\pi }{2}\,,\,0 \}$
$\{ - \frac{\pi }{2}\,,\,0\,,\,\frac{\pi }{2} \}$
$\{ \frac{\pi }{2}\,,\,0 \}$
$\{ 0\,\,,\,\,\frac{\pi }{4}\,\,,\,\frac{\pi }{2} \}$
One of the solutions of the equation $8 \sin ^3 \theta-7 \sin \theta+\sqrt{3} \cos \theta=0$ lies in the interval
If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$
If ${\sin ^2}\theta = \frac{1}{4},$ then the most general value of $\theta $ is
If $2{\tan ^2}\theta = {\sec ^2}\theta ,$ then the general value of $\theta $ is
Let $f(x)=\cos 5 x+A \cos 4 x+B \cos 3 x$ $+C \cos 2 x+D \cos x+E$, and
$T=f(0)-f\left(\frac{\pi}{5}\right)+f\left(\frac{2 \pi}{5}\right)-f\left(\frac{3 \pi}{5}\right)+\ldots+f\left(\frac{8 \pi}{5}\right)-f\left(\frac{9 \pi}{5}\right) \text {. }$Then, $T$