Trigonometry identities

[Monokuro]

How do I prove the following identities?
1. (cotx+tanx)²-2=tan²xcot²x
2. sec⁴θ-sec⁴θ=tan⁴θ+tan²θ
3. sec²θ +csc²θ=sec²θcsc²θ
Thanks

 

[Quaid]

How do I prove the following identities?

1. (cotx + tanx)² - 2 = tan²x cot²x

2. sec⁴θ - sec⁴θ = tan⁴θ + tan²θ

3.sec²θ + csc²θ = sec²θ csc²θ

Hello. We prefer one exercise per thread. Additionally, will you please proofread your post. Equations 1 and 2 are not identities, as typed.

Equation 3 is an identity. Have you proven identities before? Have you learned any of the basic identities, yet? What have you done, so far, on Equation 3? Where are you stuck?

This is a tutoring website; please follow our forum guidelines. You can start with this link to the summary page.

If you're totally stuck, try rewriting the left-hand side in terms of sine and cosine. Show us how far you get.

Otherwise, we can provide links to lessons on-line, if you like.

Cheers