If $\sqrt 2 \sec \theta + \tan \theta = 1,$ then the general value $\theta $ is
$n\pi + \frac{{3\pi }}{4}$
$2n\pi + \frac{\pi }{4}$
$2n\pi - \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{4}$
Let $\theta, 0 < \theta < \pi / 2$, be an angle such that the equation $x ^2+4 x \cos \theta+\cot \theta=0$ has equal roots for $x$. Then $\theta$ in radians is
General solution of $eq^n\, 2tan\theta \, -\, cot\theta =\, -1$ is
If $n$ is any integer, then the general solution of the equation $\cos x - \sin x = \frac{1}{{\sqrt 2 }}$ is
All the pairs $(x, y)$ that satisfy the inequality ${2^{\sqrt {{{\sin }^2}{\kern 1pt} x - 2\sin {\kern 1pt} x + 5} }}.\frac{1}{{{4^{{{\sin }^2}\,y}}}} \leq 1$ also Satisfy the equation
The number of solutions of the equation $sin\, 2x - 2\,cos\,x+ 4\,sin\, x\, = 4$ in the interval $[0, 5\pi ]$ is