Calculate-3-cosec-20-sec-20-

Question Number 140196 by mathdanisur last updated on 05/May/21

C a l c u l a t e : \sqrt{3} c o s e c 20 ° - s e c 20 °

Answered by liberty last updated on 05/May/21

\frac{\sqrt{3}}{\sin 20 °} - \frac{1}{\cos 20 °} =

\frac{2 (\sqrt{3} \cos 20 ° - \sin 20 °)}{\sin 40 °} =

\frac{4 (\frac{\sqrt{3}}{2} \cos 20 ° - \frac{1}{2} \sin 20 °)}{\sin 40 °} =

\frac{4 (\cos 30 ° \cos 20 ° - \sin 30 ° \sin 20 °)}{\sin 40 °} =

\frac{4 \cos 50 °}{\sin 40 °} = 4

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