How to solve cos^4-sin^4x/1-tan^4x=cos^4x?

Use the identity tan x = sin x/cos x. Then 1 – tan^{4}x = 1 – (sin^{4}x/cos^{4}x) = (cos^{4}x – sin^{4}x)/cos^{4}x

and (cos^{4}x – sin^{4}x)/(1 – tan^{4}x) =

(cos^{4}x – sin^{4}x) ÷ [(cos^{4}x – sin^{4}x)/cos^{4}x] = division by a fraction is multiplication by the reciprocal

(cos^{4}x – sin^{4}x) × [cos^{4}x/(cos^{4}x – sin^{4}x)] =

cos^{4}x

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