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 $f(x)=\sin{x}$.[2] Let $\sin{x}=\frac{2}{3}$. Show that $f(2x)=-\frac{4\sqrt{5}}{9}$.[5]

Accepted Answer

(a) $\mathrm{f}(x)=\sin x$. (b) $\mathrm{f}(2x)$ is undefined on the stated domain; $\sin2x=-4\sqrt5/9$.

Trigonometry - Compound and Double-Angle Identities

Trigonometry - Compound and Double-Angle Identities

Solution:

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