$3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}+4(\sin ^{6} x+\cos ^{6} x)$ is equal to

If $\tan A + \cot A = 2$,then the value of $\tan^{4} A + \cot^{4} A$ is:

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then

If $\tan x = \frac{b}{a},$ then $\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}} = $

Let $P(\alpha, \beta)$ and $Q(\gamma, \delta)$ be two points that lie on the curve $\tan^2(x+y) + \cos^2(x+y) + y^2 + 2y = 0$ in the $XY$-plane. If the distance between $P$ and $Q$ is $d$,then $\cos d =$

If $O$ is the circumcentre of the $\Delta ABC$ and $R_1, R_2$ and $R_3$ are the radii of the circumcircles of triangles $OBC, OCA$ and $OAB$ respectively,then the value of $\frac{a}{R_1} + \frac{b}{R_2} + \frac{c}{R_3}$ is equal to: