I have a test coming up and need help understanding concepts. The questions aren't for a grade just ones as examples that I needed some explanations. I appreciate it.

1. verify the following identities

(a) sinx + cosx = √2sin(x + π 4)

(b) sinx + 2cosx = √5sin(x + sin−1( 2 √5))

(c) cosx 1−sinx = 1+sinx cosx

(d) 1+cosx 1−cosx − 1−cosx 1+cosx = 4cotxcscx

(e) sinx + cosx = sinx 1−cotx + cosx 1−tanx

(f) (2sinx + cosx)2 + (2cosx−sinx)2 = 5 (g) secx−cosx + cscx−sinx−sinxtanx = cosxcotx

2. Find α if

(a) sinx−cosx = √2sin(x + α)

(b) 2sinx + 3cosx = √13sin(x + α)

(c) 3sinx + 4cosx = 5cos(x + α)

(d) −12sinx + 5cosx = 13cos(x + α)

3. Verify the identities

(a) tanx + cotx = 2csc2x

(b) 1 + tanxtan2x = sec2x

(c) sin2xcos2x = sin2x−4sin3 xcosx

4. Solve the following equations on the given domain:

(a) 5sin(3x−2)−2 = 0, D = [0,2π]

(b) 7cos(2x) = 4, D = [0,2π]

(c) 3tan(π−x) = −1, D = [0,2π]

(d) cosx = 3sinx, D = [0,2π]

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