SOLUTION: How do I prove this? (cot θ+tan θ)/cot θ=sec^2 θ Thank you

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Question 678960: How do I prove this?
(cot θ+tan θ)/cot θ=sec^2 θ
Thank you

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28cot+%28theta%29%2Btan+%28theta%29%29%2Fcot+%28theta%29=sec%5E2+%28theta%29
start with left side and prove that is equal to right side
use identities:
tan%28theta%29=++sin%28theta%29%2Fcos%28theta%29

cot%28theta%29=+1%2Ftan%28theta%29=+cos%28theta%29%2Fsin%28theta%29

so,
cot+%28theta%29%2Fcot%28theta%29%2Btan%28theta%29%2Fcot%28theta%29

=1%2B%28sin%28theta%29%2Fcos%28theta%29%29%2F%28cos%28theta%29%2Fsin%28theta%29%29


=1%2B%28sin%28theta%29sin%28theta%29%29%2F%28cos%28theta%29cos%28theta%29%29

=1%2B%28sin%5E2+%28theta%29%29%2F%28cos%5E2+%28theta%29+%29

=1%2B%28sin%5E2+%28theta%29%29%2F%28cos%5E2%28theta%29+%29

=1+%2B+tan%5E2%28theta%29........use identity 1+%2B+tan%5E2%28theta%29=+sec%5E2%28theta%29

=sec%5E2%28theta%29