Question

`1/3(sqrt(3)  cos 23^circ -  sin 23^circ)` is equal to ______.

Options

• cos 43°

• cos 7°

• `1/4 cos 53^circ`

• `2/3 cos 53^circ`

Answer 1

`1/3(sqrt(3)  cos 23^circ -  sin 23^circ)` is equal to `underlinebb(2/3 cos  53^circ)`.

Explanation:

We have, `1/3(sqrt(3)  cos 23^circ -  sin 23^circ)`

= `2/3(sqrt(3)/2 cos 23^circ - 1/2 sin 23^circ)` .

= `2/3(cos 30^circ  cos 23^circ -  sin 30^circ  sin 23^circ)`  ..`[∵ cos 30^circ = sqrt(3)/2, sin 30^circ = 1/2]`

= `2/3 cos (30^circ + 23^circ)`  ...[∵ cos (A + B) = cos A cos B – sin A sin B]

= `2/3 cos 53^circ`