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Prove cos^2(x)=1/(1+tan^2(x)) only by manipulating the LHS?
It's pretty easy to prove the equation by changing the right hand side but I want to know how to approach the question if it is only the left hand side which can be altered.
I need to be able to show that I can go from one line involving cos^2(x) to another line involving 1/(1+tan^2(x)) in a certain question.
Also, 1/sec^2(x)=1/(1+tan^2(x)) is kind of cheating since it relies on knowledge that the RHS can be converted to the LHS but not being able to show the other way around.
Figured it out.
LHS = cos^2(x)
LHS(cos^2(x) + sin^2(x)) = cos^2(x)
LHS(cos^2(x)/cos^2(x) + sin^2(x)/cos^2(x)) = 1
LHS(1 + tan^2(x)) = 1
LHS = 1/(1+tan^2(x))
LHS = RHS