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Question: \(\frac{1}{\sin 10{^\circ}} - \frac{\sqrt{3}}{\cos 10{^\circ}}\)=...

1sin⁡10∘−3cos⁡10∘\frac{1}{\sin 10{^\circ}} - \frac{\sqrt{3}}{\cos 10{^\circ}}=

A

0

B

1

C

2

D

4

Answer

4

Explanation

Solution

1sin⁡10∘−3cos⁡10∘=2(12cos⁡10o−32sin⁡10o)22(=cos⁡10o−3sin⁡10osin⁡10ocos⁡10osin⁡10ocos⁡10o)\frac{1}{\sin 10{^\circ}} - \frac{\sqrt{3}}{\cos 10{^\circ}} = \frac{2\left( \frac{1}{2}\cos 10^{o} - \frac{\sqrt{3}}{2}\sin 10^{o} \right)}{\frac{2}{2}\left( = \frac{\cos 10^{o} - \sqrt{3}\sin 10^{o}}{\sin 10^{o}\cos 10^{o}}\sin 10^{o}\cos 10^{o} \right)}

=4sin⁡(30o−10o)sin⁡20o=4sin⁡20osin⁡20o=4= \frac{4\sin(30^{o} - 10^{o})}{\sin 20^{o}} = \frac{4\sin 20^{o}}{\sin 20^{o}} = 4.