1. Giventan A = -³/₄with3/2< A < 2with andsin B = with0 < B

find:

(a) tan(2A)

(b) cos(2A)

(c) sin(A+B)

2. Find the following values. You do not need to simplify square roots, but you should not leave fractions within fractions.

1. tan(cos^-12/5)

1. sin(2tan^-13/7)

3. Use the angle-sum formula for sine to find the exact value of sin75.

4. Solve the following equations for 0 360:

(a) cos²+ cos= 0

(b) tan²(2) = 1

5. Clearly explain the following formulas. (a) Starting with the formula cos(2A) = cos²(A) sin²(A),

show that cos(2A) = 2cos²(A) 1.

(b) Starting with the formula

show that

.

(c) Hence, find theexactvalue of cos15.

6. Verify the following trigonometric identity, clearly explaining each step:

cot+ 1 = csc(cos+ sin)