Conditional trigonometric identity

A conditional trigonometric identity is a trigonometric identity that holds if specified conditions on the arguments to the trigonometric functions are satisfied. Typically such a condition says ${\textstyle \alpha +\beta +\gamma =\pi {\text{ radians}}=180^{\circ }={\text{half circle,}}}$ so that ${\textstyle \alpha ,\beta ,\gamma }$ are the three angles of a triangle.

For example:

$${\begin{aligned}&{\text{If }}\alpha +\beta +\gamma =\pi {\text{ then }}\tan \alpha +\tan \beta +\tan \gamma =\tan \alpha \tan \beta \tan \gamma .\\[5pt]&{\text{If }}\alpha +\beta +\gamma =\pi {\text{ then }}\sin(2\alpha )+\sin(2\beta )+\sin(2\gamma )=4\sin \alpha \sin \beta \sin \gamma .\end{aligned}}$$

See also

• Further "conditional" identities