Question

prove that sin^3a + cos^3a/sina + cos a = 1-1/2 sin2a

Answer 1

Answer on Question #43729 – Math – Trigonometry

prove that $\sin^3 a + \cos^3 a / \sin a + \cos a = 1 - 1/2 \sin 2a$

Answer.

$$\frac{\sin^3 \alpha + \cos^3 \alpha}{\sin \alpha + \cos \alpha} = \frac{(\sin \alpha + \cos \alpha)(\sin^2 \alpha - \sin \alpha \cos \alpha + \cos^2 \alpha)}{\sin \alpha + \cos \alpha} = 1 - \sin \alpha \cos \alpha = 1 - \frac{1}{2} \sin 2\alpha.$$

Q.E.D.

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