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)
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 = BC
b) By considering angle ACD, prove CD = [10 + BC] / [SQRT 3]
c) Use these two results to find BC
Thank you in advance!