1. Review 5.1 to 5.3

2. a) Add 3 sin2 x cos x + 2 sin2 x cos x.
b) Expand (cos x – 1)2.
cos2 x – 2cos x + 1
c) Multiply (2 sin x – 3)(3 sin x + 5).
6sin2 x + sin x - 15

3. Factor. a) 25 sin2 x - 4 (5 sin x + 2)(5 sin x – 2)
b) 2tan2x – 2tanx – 40
2(tan x – 5)(tan x + 4)
c) cos2 x sin3 x - cos2 x sin5 x
cos2 x sin3 x (1 – sin2 x) = cos4x sin3 x
d) cos x – sin2 x - 7
(cos x + 4)(cos x – 2)

4. Simplify. a) cot x sec x csc x b) cos x + sec x (cos2x + 1)/cos x
c) csc2 x – cot2 x
cot2 x + 1
sin2 x
d) – tan2x
1 + tan2x
cos2x – sin2x

5. Prove.
a) = cot2 x 1 – cos x 1 + c0s x b) sec x + tan x = cos x 1–sin x

6. Solve. a) sin x = -.872 x ≈ 4.2 + 2πk or x ≈ 5.22 + 2πk
b) 8tan x + 11 = 2 tan x + 5
x = 3π/4 + πk
c) (sin x + 1)(4cos2x – 1) = 0
x = 3π/2 + 2πk or x = π/3 + πk or x = 2π/3 + πk
d) 3cos x = 5 sin x
x ≈ πk

7. and just a few more… a) 2sec x + 1= 5 x = π/3 + 2πk or 5π/3 + 2πk
b) cos 2x = ½
x = π/6 + πk or 5π/6 + πk
c) cos x + 2 sec x = -3
x = π + 2 π k
d) sin x + 1 = cos x
x = 2 π k or x = 3π/2 + 2 π k