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  •  Value of <img alt="\sqrt{3} \csc 20^{\circ}-\sec 20^{\circ}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Csqrt%7B3%7D%20%5Ccsc%2020%5E%7B%5Ccirc%7D-%5Csec%2020%5E%7B%5Ccirc%7D"

 Value of \sqrt{3} \csc 20^{\circ}-\sec 20^{\circ} is equal to ?    

Option: 1

2 \cdot \frac{\sin 20^{\circ}}{\sin 40^{\circ}}


Option: 2

2


Option: 3

4 \cdot \frac{\sin 20^{\circ}}{\sin 40^{\circ}}


Option: 4

4


Answers (1)

best_answer

\sqrt{3} \csc 20^{\circ}-\sec 20^{\circ}=\frac{\sqrt{3}}{\sin 20^{\circ}}-\frac{1}{\cos 20^{\circ}}\\ =\frac{\sqrt{3}\cos 20^{\circ}-\sin 20^{\circ}}{\sin 20^{\circ} \cos 20^{\circ}}\\ =4 \cdot \frac{\frac{\sqrt{3}}{2}\cos 20^{\circ}-\frac{1}{2}\sin 20^{\circ}}{\sin 40^{\circ}}\\ =4 \cdot \frac{\cos 50^{\circ}}{\sin 40^{\circ}}\\ =4

Posted by

Devendra Khairwa

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