SOLUTION: prove the identities 1/(〖tan〗^2 ϴ+1)+1/(〖cot〗^2 ϴ+1)=1 i know tan^2 ϴ+1 = sec^2 ϴ and cot^2 ϴ+1 = csc^2 ϴ th

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: prove the identities 1/(〖tan〗^2 ϴ+1)+1/(〖cot〗^2 ϴ+1)=1 i know tan^2 ϴ+1 = sec^2 ϴ and cot^2 ϴ+1 = csc^2 ϴ th      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 949485: prove the identities 1/(〖tan〗^2 ϴ+1)+1/(〖cot〗^2 ϴ+1)=1
i know tan^2 ϴ+1 = sec^2 ϴ
and cot^2 ϴ+1 = csc^2 ϴ
then sec^2 ϴ is (1/cosϴ)^2
and csc^2 ϴ is (1/sinϴ)^2
cos^2 ϴ + sin^2 ϴ = 1
please help ... to prove
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
prove the identities 1/(〖tan〗^2 ϴ+1)+1/(〖cot〗^2 ϴ+1)=1
i know tan^2 ϴ+1 = sec^2 ϴ
and cot^2 ϴ+1 = csc^2 ϴ
then sec^2 ϴ is (1/cosϴ)^2
and csc^2 ϴ is (1/sinϴ)^2
cos^2 ϴ + sin^2 ϴ = 1
please help ... to prove
===============
1 more step:
1 = 1
sin^2 + cos^2 = 1 is the Pythagorean Identity.
----
i know tan^2 + 1 = sec^2
Multiply thru by cos^2
sin^2 + cos^2 = 1