Trigonometric function

1. Given that sin2A=(2tanA)/(1+tan²A). Given that angle A satisfying the equation 8-2tanA=5sin2A. Show that tanA will satisfy the equation x^3 - 4x^2 +6x - 4=0. Hence, show that tanA=2.

2a Without using calculator, show that A=54° is a solution of the equation cos3A+sin2A=0.
2b Show that cos3A=4cos³A-3cosA.
2c Using (a) and (b), find the value of sin54° and leave the answer in surd form.

3. By using the sum-to-product formula, prove that (sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A) = tan4A.