Question

`(sin20^circ +2sin40^circ)/sin70^circ=` ______.

Options

• `sqrt3`

• 1

• `1/sqrt3`

• `2sqrt3`

Answer 1

`(sin20^circ +2sin40^circ)/sin70^circ  = underline (sqrt3)`.

Explanation:

`(sin20^circ +2sin40^circ)/sin70^circ  = (sin20^circ +sin40^o + sin40^circ)/sin70^circ`

`=(2sin30^circcos10^circ+sin40^circ)/sin70^circ`

`=(cos(90^circ-80^circ)+sin40^circ)/sin70^circ`

`=(sin80^circ+sin40^circ)/sin70^circ`

`=(2sin60^circcos20^circ)/sin70^circ`

`=(2xxsqrt3/2xxcos(90^circ-70^circ))/sin70^circ`

`=(sqrt3sin70^circ)/sin70^circ`

`=sqrt3`