Let $ f(x) = \sin^3{x} + \cos^3{x}\tan{x}$, $\frac{\pi}{2}

Question

Let $ f(x) = \sin^3{x} + \cos^3{x}\tan{x}$, $\frac{\pi}{2} < x < \pi$. Show that $f(x) = \sin{x}$. Let $\sin{x} = \frac{2}{3}$. Show that $f(2x) = -\frac{4\sqrt{5}}{9}$.

Accepted Answer

(a) $f(x)=\sin x$ (b) $f(2x)=-\dfrac{4\sqrt5}9$

Trigonometry - Compound and Double-Angle Identities

Trigonometry - Compound and Double-Angle Identities

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