Question

Simplify the following:
2(csc^2θ-cot^2θ)
and
(tan^2θ-sin^2θ)/(tan^2θsin^2θ)

Answer 1

is that\[2\left( \csc ^{2}\theta -\cot ^{2} \theta \right)\]

Answer 2

yes, for the first one

Answer 3

did you rewite using sin and cos?... give that a shot and you should find it very easy.

Answer 4

I ended up getting 2?

Answer 5

Do I do that with the second equation too?

Answer 6

yeah!!! that's what I got.
And yes... that's often the thing to do with trig identites.

Answer 7

Oh! That's all there is?

Answer 8

oooh, on the 2nd one, write each numerator term over the denominator and see what you get... should look familiar.

Answer 9

with the trig things, it's often a matter of rewriting them and then recognizing a common identity or relationship which will simplify the expression.

Answer 10

I got cotθ

Answer 11

usually, using sin and cos but sometimes the other functions

Answer 12

cot?
\[\frac{ \tan ^{2} \theta}{ \tan ^{2} \theta \sin ^{2} \theta } - \frac{ \sin ^{2} \theta}{ \tan ^{2} \theta \sin ^{2} \theta }= \frac{1}{ \sin ^{2} \theta } - \frac{ 1}{ \tan ^{2} \theta } = \csc ^{2} \theta - \cot ^{2} \theta\]

Answer 13

ohh, I thought you would have to turn the tan to sin/cos

Answer 14

so you just did that one and what did you get?

Answer 15

I got cotθ, but I think your way seems a lot more logical