6. Trigonometric Identities and More Equations

If cos x = -0.750 and sin ≈ 0.6614, then tan x/2 ≈ .

Simplify each expression.

√[(1 + cos 165°)/(1 - cos 165°)]

Simplify each expression. See Example 4.

2 tan 15°/(1 - tan² 15°)

Simplify each expression.

sin 158.2°/(1 + cos 158.2°)

Simplify each expression.

±√[(1 + cos 18x)/2]

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°

Determine whether the positive or negative square root should be selected.

sin (-10°) = ± √[(1 - cos (-20°))/2]

Simplify each expression.

±√[(1 + cos 20α)/2]

Simplify each expression.

±√[(1 - cos 8θ)/(1 + cos 8θ)]

Simplify each expression. See Example 4.

cos² π/8 - 1/2

Simplify each expression.

±√[(1 - cos 5A)/(1 + cos 5A)]

Simplify each expression.

± √[(1 + cos (x/4))/2]

Simplify each expression. See Example 4.

tan 34°/2(1 - tan² 34°)

Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically.

(1 - cos 2x)/sin 2x