Express each function as a trigonometric function of x. See Example 5.

cos 4x

Find cos(s + t) and cos(s - t).

cos s = - 8/17 and cos t = - 3/5, s and t in quadrant III

Find cos(s + t) and cos(s - t).

sin s = 2/3 and sin t = -1/3, s in quadrant II and t in quadrant IV

Find cos(s + t) and cos(s - t).

cos s = √2/4 and sin t = - √5/6, s and t in quadrant IV

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos( π/2 + x) = -sin x

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos 2x = cos² x - sin² x

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos 2x = 1 - 2 sin² x

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos 2x = (cot² x - 1)/(cot² x + 1)