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. cos^2(3pi/8) - sin^2 (-3pi/8) Use the appropriate double angle formula to rewrite the given expression as the sine cosine or tangent of the corresponding double angle cos^2 (- pi/8)- sin (-3pi/8) = Find the exact of the trigonometric expression without the use of a calculator. cos^(-3pi/8) -sin^2(-3pi/8) =

Solution

cos^2(-3pi/8) -sin^2(-3pi/8)

Use the formula :cos2x = cos^2x -sin^2x

cos(2*(-3pi/8)) = cos(-3pi/4) = cos(3pi/4)

= cos(pi -pi/4) = -cospi/4 = -1/sqrt2