Verify trig identity

Question

I have been stuck on this one forever now plz help

cos2(theta) csc2(theta) + cos2(theta) sec2(theta) = csc2(theta)

 

Edit: messed up the fact that the second cos and the sec are also both squared sorry :(

Answer 1

Not as bad as it looks!

Transforming the left side:

cos²csc² + cos sec

cos²(1/sin²) + cos (1/cos)

cos²(1/sin²) + 1

 

QED

Answer 2

cos²θ csc²θ  + cosθ secθ = cos²θ (1/sin²θ) + 1

 

                                      = cos²θ /sin²θ  + sin²θ/sin²θ

 

                                      = (cos²θ + sin²θ)/ sin²θ

 

                                      = 1/sin²θ = csc²θ

 

Answer 3

A good first step when proving trig identities is to write everything in terms of sin and cos. So csc^2(theta) is 1/sin^2(theta), etc. Once you do that step you are much closer to proving this identity. 

 

One more tip: Keep a sheet of trig identities handy. Most teachers won't require you to have them all memorized. 

 

Good luck!