A-MTH Trigonometry (Quick)

1. Prove that (a) csc x -sin x = cos x cot x , (b) (sin x + cos x)^2/(sin x -cos x)^2 = tan(45+x)/tan(45-x).
2. Given that sin B = k sin (2a+B), prove that tan (a+B) = (1+k/1-k)tan a.
3. (a)Prove that sin^4 A + cos^4 A = (1/4)(3+cos4A)
(b)Hence find the general solution of sin^4 A + cos^4 A = 5/6.(Give your answer correct to the nearest 0.1 degree.)
5. Find the general solution of the equation sin5θ + sin3θ = cosθ.
6. Show that sin3θ/sinθ + cos3θ/cosθ = 4 cos 2θ.