AM-2602

Proving identities

A Math · Secondary 4 · Hard · Proving identities

Prove the identity

\cot \theta - \sin \theta = \csc \theta - 2\sin \theta.

Proof using $\cot \theta = \dfrac{\cos \theta}{\sin \theta}$ and $\sin^2\theta+\cos^2\theta=1$ is correct
Identity is false for all $-90^\circ<\theta<90^\circ$
Identity holds only when $\theta = 45^\circ$
Identity simplifies to $\sin \theta = \cos \theta$

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