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

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

May 1st, 2015

Use the identity tan x = sin x/cos x. Then 1 – tan4x = 1 – (sin4x/cos4x) = (cos4x – sin4x)/cos4x

and (cos4x – sin4x)/(1 – tan4x) = 

(cos4x – sin4x) ÷ [(cos4x – sin4x)/cos4x] =                        division by a fraction is multiplication by the reciprocal

(cos4x – sin4x) × [cos4x/(cos4x – sin4x)] = 

cos4x


May 1st, 2015

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