If $\sin 3A = \cos (A - 26^{\circ})$,where $3A$ is an acute angle,then the value of $A$ is (in $^{\circ}$)

$\sin (\beta + \gamma - \alpha ) + \sin (\gamma + \alpha - \beta ) + \sin (\alpha + \beta - \gamma ) - \sin (\alpha + \beta + \gamma ) = $

Let $f$ be an odd function defined on the set of real numbers such that for $x \geq 0$,$f(x) = 3 \sin x + 4 \cos x$. Then $f(x)$ at $x = -\frac{11\pi}{6}$ is equal to:

If $\tan \alpha = (1 + 2^{-x})^{-1}$ and $\tan \beta = (1 + 2^{x+1})^{-1}$, then $\alpha + \beta$ equals:

$\sin ^2 \frac{\pi }{8} + \sin ^2 \frac{3\pi }{8} + \sin ^2 \frac{5\pi }{8} + \sin ^2 \frac{7\pi }{8} = $

The circular measure of an angle of an isosceles triangle is $\frac{5 \pi}{9}$. The circular measure of one of the other angles must be