# double angle identity

• Mar 31st 2009, 06:20 AM
amanda0603
double angle identity
4sin2Xcos2X
A) 1/2sin16X
B) cos8X
C) cos4X
D)2sin4X

determine whether the equation is an identity. if an identity prove it.

(sinx+cosx)^2=1

find all solutions in [0,2pi)
tanxsecx=squareroot of 2.

2sinxcosx+cosx=0

thank you so much in advanced!!!!!
• Mar 31st 2009, 09:07 AM
Stonehambey
Quote:

Originally Posted by amanda0603
4sin2Xcos2X
A) 1/2sin16X
B) cos8X
C) cos4X
D)2sin4X

use $\displaystyle \sin 2x = 2\sin x \cos x$

Quote:

determine whether the equation is an identity. if an identity prove it.

(sinx+cosx)^2=1
Expand this and compare with $\displaystyle \sin^2 x + \cos^2 x = 1$, what can you deduce?

Quote:

find all solutions in [0,2pi)
tanxsecx=squareroot of 2.

Try using $\displaystyle \tan x = \frac{\sin x}{\cos x}$ and $\displaystyle \sec x = \frac{1}{\cos x}$

Quote:

2sinxcosx+cosx=0

thank you so much in advanced!!!!!
Pull out a $\displaystyle \cos x$ and solve each part individually (set them equal to zero)

Good luck :)