use algebra to prove the identity?

Question

cos(2x) = (1-(tan x)^2)) / (1+(tan x)^2))

Answer 1

cos(2x) = cos(x + x) = (cosx)^2 - (sinx)^2 = (1 - (tanx)^2)/((secx)^2) by dividing (cosx)^2 throughout = (1-(tan x)^2)) / (1+(tan x)^2))

Answer 2

in case you multiply the two factors via one million/one million + cos(x) then you somewhat get sin(x)/one million-cos^(2)x= one million/sin(x) through identity sin^(2)x + cos^(2)x = one million (examine as sin squared x plus cosine squared x equals one million) then you somewhat comprehend that one million - cos^(2)x is comparable to sin^(2)x, so once you replace that for the time of, you get sin(x)/sin^(2)x = sin(x), that's a genuine assertion because of the fact the former is reminiscent of x/x^(2), that's purely one million/x, that's reminiscent of the latter. wish this helps :) *notice: as quickly as I write sin^(2)x, the sin function is squared, no longer the x. sin^(2)x = sin(x) circumstances sin(x)

Answer 3

RHS
[ (1 - (sin x / cos x)² / (1 + (sin x / cos x)² ]
[(cos²x - sin²x) / cos²x ] / [(cos²x + sin²x) / cos²x ]
[ cos 2x / cos²x ] [ cos²x / 1 ]
cos 2x

LHS
cos 2x