Question

sinA+sin2A/1+cosA+cos2A=tanA

Answer 1

Answer to Question #86062 – Math – Trigonometry

Question

Prove that

$$\frac {\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \tan A$$

Solution

$$\frac {\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \frac {\sin A + 2 \sin A \cos A}{1 + \cos A + 2 \cos^ {2} A - 1} (\sin 2A = 2 \sin A \cos A; \cos 2A = 2 \cos^ {2} A - 1)$$ $$\frac {\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \frac {\sin A (1 + 2 \cos A)}{\cos A + 2 \cos^ {2} A}$$ $$\frac {\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \frac {\sin A (1 + 2 \cos A)}{\cos A (1 + 2 \cos A)}$$ $$\frac {\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \frac {\sin A}{\cos A}$$ $$\frac {\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \tan A$$

Q.E.D.

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