Rewrite the expression as a sine cosine or tangent of a doub

Rewrite the expression as a sine, cosine or tangent of a double-angle. then find the exact vaule of the trigonometric expression without the use of the calculator.

use the appropiate double-angle formula to write the given expression as the sine,cosine or tangent of the corresponding double-angle

2 tan(-5pi/6)/1-tan^2(-5pi/6)=

find the exact value of the trigonometric expression without the help of a calculator.

2 tan(-5pi/6)/1-tan^2(-5pi/6)=

Solution

tan(-5pi/6)/(1-tan^2(-5pi/6))

This is of the form

tan A/(1-tan^2 A)=tan 2A

Therefore we get tan(2*-5pi/6)=tan(-5pi/3)=-tan (5pi/3) = -(-sqrt3)=sqrt3