Question

In ∆ABC right angled at B, if tan A= `sqrt3`, then cos A cos C - sin A sin C = ______.

Options

• -1

• 0

• 1

• `sqrt3/2`

Answer 1

In ∆ABC right angled at B, if tan A= `sqrt3`, then cos A cos C - sin A sin C = 0.

Explanation:-

tan A= `sqrt3` = tan 60° so ∠A=60°, Hence ∠C = 30°

So cos A cos C - sin A sin C = `(1/2xxsqrt3/2)-(sqrt3/2xx1/2)=0`