No. of solution of equation $sin^{65}x\, -\, cos^{65}x =\, -1$ is, if $x \in (-\pi , \pi )$
$3$
$4$
$2$
$1$
The real roots of the equation $cos^7x\, +\, sin^4x\, =\, 1$ in the interval $(-\pi, \pi)$ are
If $\cos \,x = \frac{{2\cos y – 1}}{{2 – \cos y}},x,\,y\, \in \,\left( {0,\pi } \right),$ then $tan(x/2)cot(y/2) =$
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \quad \cos (\lambda \alpha)}{\sin \alpha}=\lambda-1$,holds for all real $\alpha$ which are not integral multiples of $\pi / 2$ is
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
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