SOLUTION: Establish the Identity: (secθ-tanθ)^2+1 / secθcscθ-tanθcscθ =2tanθ

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Question 769871: Establish the Identity:
(secθ-tanθ)^2+1 / secθcscθ-tanθcscθ =2tanθ
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Establish the Identity:
(secθ-tanθ)^2+1 / secθcscθ-tanθcscθ =2tanθ
start with left-hand side
(sec^2-2sectan+tan^2+1)/(seccsc-tancsc)
tan^2+1=sec^2
(sec^2-2sectan+sec^2)/(csc(sec-tan))
(2sec^2-2sectan)/(csc(sec-tan))
2sec(sec-tan)/(csc(sec-tan))
2sec/csc=2(1/cos)/(1/sin)=2sin/cos=2tan
verified:
left-hand side =right-hand side