Show-that-3-cosec20-sec20-4-

Question Number 15641 by tawa tawa last updated on 12/Jun/17

Show that .

\sqrt{3} (cosec 20) - \sec 20 = 4

Answered by mrW1 last updated on 12/Jun/17

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

= \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}

= \frac{4 \sin 40}{\sin 40}

= 4

Commented by tawa tawa last updated on 12/Jun/17

God bless you sir .