Basic Trigonometric Identities

If $xy+yz+zx=1,$ then $\sum \frac{x+y}{1-xy}=$

The expression ${\left(\frac{\cos A+\cos B}{\sin A-\sin B}\right)}^n+{\left(\frac{\sin A+\sin B}{\cos A-\cos B}\right)}^n=$

Find the value of $\tan 9°-\tan 27°-\tan 63°+\tan 81°$.

$2\sin \left(\frac{5\pi }{12}\right)\sin \left(\frac{\pi }{12}\right)$ equal to

In a right angled triangle, the hypotenuse is four times as long as the perpendicular drawn to it from the opposite vertex. One of the acute angles is

$\sin 10°+\sin 20°+\sin 30°+\dots \dots +\sin 360°$ is equal to

If $A={\cos }^2\theta +{\sin }^4\theta ,$ then for all real values of $\theta$

$\cos 52°+\cos 68°+\cos 172°=$

If $y=\frac{2\sin \alpha }{1+\cos \alpha +\sin \alpha }$, then $\frac{1-\cos \alpha +\sin \alpha }{1+\sin \alpha }$ is equal to

If $A+B+C=\pi ,$ then $\tan A+\tan B+\tan C$ equals

If $\sin 2\theta +\sin 2\varphi =\frac{1}{2}$ and $\cos 2\theta +\cos 2\varphi =\frac{3}{2}$ then ${\cos }^2\left(\theta -\varphi \right)$ is equal to

If $n=\frac{\pi }{4\alpha },$ then $\tan \alpha \tan 2a\tan 3\alpha ....\tan \left(2n-1\right)\alpha$ is equal to

If $\cos 2B=\frac{\cos \left(A+C\right)}{\cos \left(A-C\right)},$ then $\tan A, \tan B \& \tan C$ are in

If $2y\cos \theta =x\sin \theta$ and $2x\sec \theta -ycosec\theta =3,$ then $x^2+4y^2=$

If $\sin \left(y+z-x\right), \sin \left(z+x-y\right)$ and $\sin \left(x+y-z\right)$ are in $\mathrm{A}.\mathrm{P}.$ (with $x, y, z\ne \frac{\mathrm{\pi }}{2}$), then $\tan x, \tan y$ and $\tan z$ are in

The value of $\tan 3A-\tan 2A-\tan A$ is equal to

If $\frac{\cos A}{\cos B}=n, \frac{\sin A}{\sin B}=m,$ then $\left(m^2-n^2\right){\sin }^{2}B=$

If $\theta +\varphi =\alpha$ and $\tan \theta =k\tan \varphi ,$ then $\sin \left(\theta -\varphi \right)=$

The value of $\tan A+\tan \left(60°+A\right)-\tan \left(60°-A\right)$ is

If $\tan \theta =\sqrt{n}$ for some non-square natural number $n$, then $\sec 2\theta$ is