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Question Number 157884 by HongKing last updated on 29/Oct/21

$$\frac{1}{\sin \left(10°\right)}-4\sin \left(70°\right)=?$$

Answered by tounghoungko last updated on 29/Oct/21

$$\frac{1}{\sin 10°}-4(\frac{\sqrt{3}}{2}\cos 10°+\frac{1}{2}\sin 10°)$$$$=\frac{1}{\sin 10°}-2\sqrt{3}\cos 10°-2\sin 10°$$$$=\frac{1-2\sqrt{3}\sin 10°\cos 10°-2\sin {}^{2}10°}{\sin 10°}$$$$=\frac{1-\sqrt{3}\sin 20°-2(\frac{1}{2}-\frac{1}{2}\cos 20°)}{\sin 10°}$$$$=\frac{\cos 20°-\sqrt{3}\sin 20°}{\sin 10°}$$$$=\frac{2(\frac{1}{2}\cos 20°-\frac{\sqrt{3}}{2}\sin 20°)}{\sin 10°}$$$$=\frac{2\cos 80°}{\sin 10°}=2.$$

Commented by HongKing last updated on 29/Oct/21

$$\mathrm{alot}\mathrm{thankyou}\mathrm{sir}$$

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