TRIG Identities and Equations

These are the problems I have trouble with while doing a practice on this topic.

1. Factor the expression and use fundamental identities to simplify:

cos^(2)x csc^(2)x - cos^(2)x

2. Find all solutions in the interval [0 , 2pi)

tan^(2)θ = (-3/2)secθ

3. Find an expression that completes the identity

[2sin^(2)x + cos(2x)] / csc(x) =

It would be helpful if u could explain step by step. I'm not just looking for answers. Thanks

Re: TRIG Identities and Equations

In the first one, take out as a factor, what do you get?

For the second, create a quadratic using what do you get?

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Re: TRIG Identities and Equations

Re: TRIG Identities and Equations

In 3 use the identity cos2x=1-2sin^(2)x

Re: TRIG Identities and Equations

Re: TRIG Identities and Equations

thanks so much. I'm still stuck with #1.

I got 2 answers, cos^2x*cot^2x and cos^4x/sin^2x

but don't know which one is correct and simplified.

Re: TRIG Identities and Equations

Both your answers equal one another (because cotx=cosx/sinx)

Re: TRIG Identities and Equations

Re: TRIG Identities and Equations