Find all solutions in [0,2pi)... sin(2x)sin(x)=cos(x)
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Find all solutions in [0,2pi)... sin(2x)sin(x)=cos(x)

Find all solutions in [0,2pi)... sin(2x)sin(x)=cos(x)

[From: ] [author: ] [Date: 11-05-10] [Hit: ]
......
if you could show me step by step please

-
Start by using the very useful identity sin(2x) = 2sin(x)cos(x). We can now write

2sin(x)cos(x)sin(x) = cos(x)
2cos(x)sin^2(x) = cos(x)
2cos(x)sin^2(x) - cos(x) = 0
cos(x)*(2sin^2(x) - 1) = 0

If either factor is equal to zero, the product would be equal to zero. So now solve cos(x) = 0 and 2sin^2(x) - 1 = 0 (or sin^2(x) = 1/2) on the given interval, and then check the answers in the original equation.
1
keywords: cos,sin,pi,solutions,all,in,Find,Find all solutions in [0,2pi)... sin(2x)sin(x)=cos(x)
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .