If $A + B + C = \pi ,$ then $\frac{{\cos A}}{{\sin B\sin C}} + \frac{{\cos B}}{{\sin C\sin A}} + \frac{{\cos C}}{{\sin A\sin B}} = $

If $\frac{{\sin^4 A}}{a} + \frac{{\cos^4 A}}{b} = \frac{1}{{a + b}},$ then the value of $\frac{{\sin^8 A}}{{a^3}} + \frac{{\cos^8 A}}{{b^3}}$ is equal to

For $A = 133^\circ$,$2\cos \frac{A}{2}$ is equal to

If $\cos A + \cos B = \cos C$ and $\sin A + \sin B = \sin C$,then the value of the expression $\frac{\sin(A + B)}{\sin 2C}$ is:

If $\tan A + \sin A = m$ and $\tan A - \sin A = n,$ then $\frac{(m^2 - n^2)^2}{mn} = $

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to