# Trig. Eqautions

• May 4th 2006, 07:49 PM
CONFUSED_ONE
Trig. Eqautions
how would you simplify this trig. equation.

(1+sec2x)(cot2x)

*note: the blue 2's are squared.

i did it and the final answer i got is 2cot2x
• May 4th 2006, 10:40 PM
TD!
There is nothing to solve. You either forgot something, or perhaps meant 'simplify'?
• May 5th 2006, 05:22 AM
CONFUSED_ONE
lol. Yes, I meant simplify.
• May 5th 2006, 05:51 AM
TD!
Then your answer is wrong. I don't think there's a lot to simplify though, depends on where you want to go with it. You can simplify it to cot²x+csc²x for example.
• May 5th 2006, 02:47 PM
ticbol
Quote:

Originally Posted by CONFUSED_ONE
how would you simplify this trig. equation.

(1+sec2x)(cot2x)

*note: the blue 2's are squared.

i did it and the final answer i got is 2cot2x

Here is one way.

Let U = (1 +sec^2(x))*cot^2(x)
So,
U = cot^2(x) +[sec^2(x) *cot^2(x)]
U = cot^2(x) + [1/cos^2(x) *cos^2(x)/sin^2(x)]
U= cot^2(x) +1/sin^2(x)
U = cot^2(x) +csc^2(x) --------(i)

The trig identity,
sin^2(x) +cos^2(x) = 1
Divide both sides by sin^2(x),
1 +cot^2(x) = csc^2(x)
Rearrange,
1 = -cot^2(x) +csc^2(x) ---------(ii)