# Simplifying trig expression

• Jan 12th 2010, 01:44 AM
Paymemoney
Simplifying trig expression
Hi
A few question i am stuck on and need help:
1)$\displaystyle \frac{4sin^2(x)-4sin^4(x)}{sin(2x)}$
this is what i have done but it is incorrect.
$\displaystyle =\frac{4sin^2(x)(1-sin^2(x))}{sin(2x)}$
$\displaystyle =\frac{4sin^2(x)(cos^2(x))}{2sin(x)cos(x)}$
$\displaystyle =2sin(x)cos(x)$

2)$\displaystyle \frac{1}{2}sin(x)cos(x)$

3)$\displaystyle \frac{tan(x)}{1-tan^2(x)}$

P.S
• Jan 12th 2010, 02:04 AM
differentiate
not sure what you want to simplify the expression to. im just guessing,

1) following on,
sin2a

2) (1/2)sinxcosx = 1/4(2sinxcosx) = (1/4)sin2a

3) tanx/(1-tan^2x) = 1/2[(2tanx)/(1-tan^2x)] = 1/2tan2x
• Jan 12th 2010, 02:12 AM
Paymemoney
Quote:

Originally Posted by differentiate
not sure what you want to simplify the expression to. im just guessing,

1) following on,
sin2a

2) (1/2)sinxcosx = 1/4(2sinxcosx) = (1/4)sin2a

3) tanx/(1-tan^2x) = 1/2[(2tanx)/(1-tan^2x)] = 1/2tan2x

yeh, thanks that makes sense now.