Rewrite the expression as the some cosine or tangent of a do

Rewrite the expression as the some cosine or tangent of a double angle Then find exact value of the trigonometric expression without the use of a calculator. 2 sin (- pi/3) cos (-pi/3) Use the appropriate double angle formula to rewrite the given expression as the sine cosine or tangent of the corresponding double angle 2 sin (- pi/3) cos (pi/3) = Find the exact of the trigonometric expression without the use of a calculator.

Solution

2sin(-pi/3)cos(-pi/3)

As per formula: sin2x = 2sinxcosx

So, 2sin(-pi/3)cos(-pi/3) = sin(2*(-pi/3)) = -sin2pi/3

= -sin(pi-pi/3) = -sinpi/3

= -sqrt3/2