Trigonometric Identities

Match the column conversion: the product $2\sin 75^{\circ }\cos 15^{\circ }$, when transformed by the pro...

If $\sin \theta +\cos \theta =\frac{1}{5}$ for an angle $\theta$ lying in the second quadrant, then ...

When the expression $\frac{1-\cos 2\theta +\sin 2\theta }{1+\cos 2\theta +\sin 2\theta }$ is sim...

The identity 1 + tan²θ equals

The identity sin²θ + cos²θ equals

If $\cos \theta =\frac{3}{5}$ with $\theta$ in the first quadrant, then applying the half-angle iden...

By repeatedly using the triple-angle identity, the exact value of $\sin 3\theta$ when $\sin\theta = ...

Given that ${\tan }^{-1}x+{\tan }^{-1}y=\frac{\pi }{4}$ holds for positive reals with $xy<1$, the e...

How many distinct values of $x$ in the open interval $(0,\pi )$ satisfy the equation $\sin x + \sqrt...

In a triangle with sides $a$, $b$, $c$ and semiperimeter $s$, the area computed by Heron's formula f...

Applying the sine rule in a triangle where angle $A=30^{\circ }$, angle $B=45^{\circ }$, and the side ...

Statement based: assertion that ${\sin }^{-1}(\sin \frac{2\pi }{3})=\frac{2\pi }{3}$ and reason that arc...