6. Trigonometric Identities and More Equations

In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° - sin² 15°

Given $\(\tan\]\theta\)=\(\frac{5}{12}\)$ and 0 < $\(\theta\)$ < $\(\frac{\pi}{2}\)$, find $\(\cos\[\left\)(2\(\theta\]\right\))$.

In Exercises 1–6, use the figures to find the exact value of each trigonometric function.

sin 2θ

Find values of the sine and cosine functions for each angle measure.

2x, given tan x = 5/3 and sin x < 0

Find values of the sine and cosine functions for each angle measure.

2θ, given cos θ = (√3)/5 and sin θ > 0

Find values of the sine and cosine functions for each angle measure.

θ, given cos 2θ = 3/4 and θ terminates in quadrant III

Find values of the sine and cosine functions for each angle measure.

θ, given cos 2θ = 2/3 and 90° < θ <180°

Simplify each expression. See Example 4.

2 tan 15°/(1 - tan² 15°)

Match each expression in Column I with its value in Column II.

cos² (π/6) - sin² (π/6)

Simplify each expression. See Example 4.

1 - 2 sin² 22 ½°

Simplify each expression. See Example 4.

cos² π/8 - 1/2

Simplify each expression. See Example 4.

tan 34°/2(1 - tan² 34°)