Trig Identity - How to solve? Cross Multiply? (secθ+1)/tanθ=tanθ/(secθ-1)?
I just cross multiplied to come up with (secθ+1)(secθ-1)=tan^2(θ) then sec^2(θ) - 1 = tan^2(θ) and finally tan^2(θ)=tan^2(θ). But I don't think that this is the correct way to solve it.
The original problem is as follows: (secθ+1)/tanθ=tanθ/(secθ-1).
Thanks for the help!
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No! Cross multiplication is definitely not acceptable. This is because you must not assume the correctness of something that you are trying to prove because starting with a false statement it is sometimes possible to end with a true one.
However working as you suggest is an acceptable way of leading you to the steps of a proper proof. Therefore what you did would be your rough working and your answer would be set out with it in reverse, i.e.
(secx)^2 - 1 = (tanx)^2
(secx - 1)(secx + 1) = (tanx)^2
(secx + 1)/tanx = tanx/(secx - 1)
if you are trying to prove the result
start from the L.H.S
introduce the conjugate (secθ-1) and simplify