The value of the expression $1 - \frac{\sin^2 y}{1 + \cos y} + \frac{1 + \cos y}{\sin y} - \frac{\sin y}{1 - \cos y}$ is equal to

If $\sin \alpha = \frac{8}{17}, 0 < \alpha < 90^{\circ}$ and $\tan \beta = \frac{5}{12}, 0 < \beta < 90^{\circ},$ then $\cos (\alpha - \beta)$ is

If ${x_1}, {x_2}, {x_3}, ..., {x_n}$ are in $A.P.$ whose common difference is $\alpha$,then the value of $\sin \alpha (\sec {x_1}\sec {x_2} + \sec {x_2}\sec {x_3} + ... + \sec {x_{n - 1}}\sec {x_n}) = $

Number of integral values of $\lambda$ for which $f(x) = \sqrt{\ln(2\lambda \cos x + 5)}$ is defined for all $x \in R$ is

$\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \cdot \log \sin 3^{\circ} \cdot \ldots \cdot \log \sin 179^{\circ} = ?$

$\sin 20^\circ \sin 40^\circ \sin 60^\circ \sin 80^\circ = $ (in $/16$)