Question

`sqrt(3)  "cosec"  20^circ - sec 20^circ` is equal to ______.

पर्याय

• 2

• 2 sin 20° cosec 40°

• 4

• 4 sin 20° cosec 40°

Answer 1

`sqrt(3)  "cosec"  20^circ - sec 20^circ` is equal to 4.

Explanation:

`sqrt(3)  "cosec"  20^circ - sec 20^circ`

= `(tan 60^circ)/(sin 20^circ) - 1/(cos 20^circ)`

= `(sin 60^circ  cos 20^circ -  sin 20^circ  cos 60^circ)/(cos 60^circ  sin 20^circ  cos 20^circ)`

= `(sin 40^circ)/(cos 60^circ  sin 20^circ  cos 20^circ)`

= `(2  sin 20^circ  cos 20^circ)/(1/2 (sin 20^circ  cos 20^circ))`

= 4