The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is
$5$
$6$
$7$
$8$
The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to
If the equation $tan^4x -2sec^2x + [a]^2 = 0$ has atleast one solution, then the complete range of $'a'$ (where $a \in R$ ) is
(Note : $[k]$ denotes greatest integer less than or equal to $k$ )
$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $
One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval
The value of expression $\frac{{2(\sin {1^o} + \sin {2^o} + \sin {3^o} + ..... + \sin {{89}^o})}}{{2(\cos {1^o} + \cos {2^o} + .... + \cos {{44}^o}) + 1}}$ equals