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

Write the expression as the sine, cosine, or tangent of a double-angle. Then find the exact value of the expression. cos^2 180 degree - sin^2 180 degree Which expression is cos^2 180 degree - sin^2 180 degree equal to? sin 180 degree cos 180 degree sin 360 degree cos 360 degree The exact value of the expression is. (Simplify your answer including any radicals. Use integers or fractions for any numbers in the expression. Rationalize the denominator.)

Solution

cos^2 180 - sin^2 180

this expression is of the form

cos^2A - sin^2A

which is equal to cos 2A

therefore the given expression is equal to

cos 2(180)= cos 360

And the exact value of cos 360=1