SOLUTION: 1. Solve algebraically the equation 15sin2x°=10cosx° for 0&#8804;x<360 Can you provide full working. Andy.

Algebra ->  Equations -> SOLUTION: 1. Solve algebraically the equation 15sin2x°=10cosx° for 0&#8804;x<360 Can you provide full working. Andy.      Log On


   

Question 388619: 1. Solve algebraically the equation 15sin2x°=10cosx° for 0≤x<360
Can you provide full working.
Andy.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
15 sin 2x = 10 cos x. By double-angle formula, sin 2x = 2 sin x cos x, so

30 sin x cos x = 10 cos x. Move 10 cos x to the other side and divide by 10

3 sin x cos x - cos x = 0

cos x (3 sin x - 1) = 0

cos x = 0 or sin x = 1/3

x = 90, 270, or x = arcsin (1/3)