If $\cos 3\theta = \alpha \cos \theta + \beta {\cos ^3}\theta ,$ then $(\alpha ,\beta ) = $
$(3,\,4)$
$(4,\,3)$
$( - 3,\,4)$
$(3,\, - 4)$
If $cosA + cosB = cosC,\ sinA + sinB = sinC$ then the value of expression $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ is
$\frac{{\sec 8A - 1}}{{\sec 4A - 1}} = $
Let $\alpha ,\beta $ be such that $\pi < (\alpha - \beta ) < 3\pi $. If $\sin \alpha + \sin \beta = - \frac{{21}}{{65}}$ and $\cos \alpha + \cos \beta = - \frac{{27}}{{65}},$ then the value of $\cos \frac{{\alpha - \beta }}{2}$ is
If $A, B, C$ are angles of a triangle, then $\sin 2A + \sin 2B - \sin 2C$ is equal to
The value of $\cos 15^\circ - \sin 15^\circ $ is equal to