Trigonometric Identities - Examples & Applications

Interactive Identity Verifier

Use this tool to interactively construct and verify trigonometric identities by selecting correct substitutions.

Adjust the angle to see that $\sin^2\theta + \cos^2\theta$ always equals 1.

Angle (θ): 45°

cos(45°)0.7071

sin(45°)0.7071

Pythagorean Theorem

cos²θ + sin²θ =1

(0.5000) + (0.5000) ≈ 1

Solved Problems

Problem 1: Prove the identity

(1 + \tan^2 x) \cos^2 x = 1

0 of 3 Steps Completed

Problem 2: Prove that

\sin x \cot x = \cos x

0 of 2 Steps Completed

Problem 3: Find the exact value of

\cos(105^\circ)

0 of 3 Steps Completed