The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is
$n\pi $
$2n\pi + \frac{{3\pi }}{4}$
$2n\pi $
$(2n + 1)\,\pi $
The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :
The set of values of $x$ satisfying the equation,${2^{\tan \,\,\left( {x\,\, - \,\,{\textstyle{\pi \over 4}}} \right)}}$ $- 2$${\left( {0.25} \right)^{\frac{{{{\sin }^2}\,\left( {x\,\, - \,\,{\textstyle{\pi \over 4}}} \right)}}{{\cos \,\,2x}}}}$ $+ 1 = 0$, is :
If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are
The equation $\sqrt 3 \sin x + \cos x = 4$ has
Let $f(x) = \cos \sqrt {x,} $ then which of the following is true