Trigonometric Identities — Formula Sheet

\sin A=BC/AC

\cos A=AB/AC

\tan A=BC/AB

\operatorname{cosec} A=AC/BC

\sec A=AC/AB

\sin \theta=1/\operatorname{cosec} \theta, \operatorname{cosec} \theta=1/\sin \theta

\cos \theta=1/\sec \theta, \sec \theta=1/\cos \theta

\tan \theta=1/\cot \theta, \cot \theta=1/\tan \theta

\tan \theta=\sin \theta/\cos \theta

\cot \theta=\cos \theta/\sin \theta

\sin^{2} A+\cos^{2} A=1

1+\tan^{2} A=\sec^{2} A

1+\cot^{2} A=\operatorname{cosec}^{2} A

Step 1: Start with L.H.S. or R.H.S.

Step 2: Change the form using identities, rationalization, perfect squares, algebraic formulae, or L.C.M.

Step 3: Simplify the other side if necessary

Step 4: Equate L.H.S. and R.H.S.

Step 5: If an algebraic expression is to be proved, substitute trigonometric values and then prove L.H.S = R.H.S.

tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.