Question

The value of cot 70° + 4 cos 70° is ______.

Options

• `1/sqrt(3)`

• `sqrt(3)`

• `2sqrt(3)`

• `1/2`

Answer 1

The value of cot 70° + 4 cos 70° is `underlinebb(sqrt(3))`.

Explanation:

Now, cot 70° + 4 cos 70°

= `(cos 70^circ +  4  sin 70^circ  cos 70^circ)/sin 70^circ`

= `(cos 70^circ +  2  sin 140^circ)/sin 70^circ`

= `(cos 70^circ +  2 sin(180^circ - 40^circ))/sin 70^circ`

= `(sin 20^circ +  sin 40^circ +  sin 40^circ)/sin 70^circ`

= `(2  sin 30^circ  cos 10^circ +  sin 40^circ)/sin 70^circ`

= `(sin 80^circ +  sin 40^circ)/sin 70^circ`

= `(2  sin 60^circ  cos 20^circ)/sin 70^circ`

= `sqrt(3)`