Trigonometric Relations/Identities help

Please help me solve these:

1a) If tan(A) = 3/4, show that sin(A) = 3/4cos(A)

1b) Therefore, evaluate:

[4sin(A) - cos(A)] / [8sin(A) + 5cos(A)]

2) Solve without a calculator, show working

a) sin(60) x tan(45)

b) 9tan^2(30)

c) 6cos(60) x sin(30)

3) If sin^2(x) = 7/8, find cos^2(x)

4) If cos^2(x) = 0.36, fins sin^2(x)

5) Find tan x if cos x = 8/17 and sin x = 15/17

The last one is as an optional challenge, please help me if you can.

6) ACD is a right angled triangle, where B is a point on AC, angle CAD = 30 deg, angle CBD = 60 deg and AB = 10.

a) By considering angle BCD, prove CD = $\displaystyle SQRT 3$ BC

b) By considering angle ACD, prove CD = [10 + BC] / [SQRT 3]

c) Use these two results to find BC

Thank you in advance!