Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$

If $\sec 4\theta - \sec 2\theta = 2$, then the general value of $\theta $ is

Solve $\cos x=\frac{1}{2}$

The set of values of $‘a’$ for which the equation, $cos\, 2x + a\, sin\, x = 2a - 7$ possess a solution is :

If $\sin 2\theta = \cos 3\theta $ and $\theta $ is an acute angle, then $\sin \theta $ is equal to

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