6. Trigonometric Identities and More Equations

Simplify each expression. See Example 4.

⅛ sin 29.5° cos 29.5°

Simplify each expression. See Example 4.

cos² 2x - sin² 2x

Verify that each equation is an identity.

(sin 2x)/(2sin x) = cos² (x/2) - sin² (x/2)

Verify that each equation is an identity.

cos x = (1 - tan² (x/2))/(1 + tan² (x/2))

Write each expression as a sum or difference of trigonometric functions. See Example 7.

2 cos 85° sin 140°

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

(2 tan (π/3))/(1 - tan² (π/3))

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

2θ, given cos θ = -12/13 and sin θ > 0

In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 15 sin θ = -------- , θ lies in quadrant II. 17

Use the given information to find the exact value of each of the following: $\cos 2\theta$

$\sin \theta =\frac{12}{13},\theta \text{ lies in quadrant II.}$

Use the given information to find the exact value of each of the following: $\sin 2\theta$

$\sin \theta =\frac{12}{13},\theta \text{ lies in quadrant II.}$

Use the given information to find the exact value of each of the following: $\tan 2\theta$

$\sin \theta =\frac{12}{13},\theta \text{ lies in quadrant II.}$

Use the given information to find the exact value of each of the following: $\tan 2\theta$

$\cos \theta =\frac{24}{25},\theta \text{ lies in quadrant IV.}$