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

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- May 4th 2006, 08:49 PMCONFUSED_ONETrig. 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, 11:40 PMTD!
There is nothing to solve. You either forgot something, or perhaps meant 'simplify'?

- May 5th 2006, 06:22 AMCONFUSED_ONE
lol. Yes, I meant simplify.

- May 5th 2006, 06:51 AMTD!
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, 03:47 PMticbolQuote:

Originally Posted by**CONFUSED_ONE**

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)

Add (i) and (ii),

U +1 = 2csc^2(x)

Hence,

U = 2csc^2(x) -1

Therefore,

(1 +sec^2(x))*cot^2(x) = 2csc^2(x) -1 -----------answer.

Or,

Subtract (ii) from (i),

U -1 = 2cot^2(x)

Hence,

U = 2cot^2(x) +1

Therefore,

(1 +sec^2(x))*cot^2(x) = 2cot^2(x) +1 -----------answer.