Question

cos^2theta - sin^2 theta = tan^ alpha
then prove that
cos^2 alpha - sin^2 alpha = tan^ alpha
Don't post anything else I'll report you​

Answer 1

Given If tan^2 alpha= cos^2 beta-sin^2beta, then prove cos^2alpha-sin^2alpha= tan^2 beta

We need to know the formula

cos2x = 1 - tan^2 x /1 + tan ^2 x

cos2x = cos^2 x - sin ^2 x

Now it is given

tan ^2 alpha = cos^2 beta - sin^2 beta

tan^2 alpha = cos2 beta

tan^2 alha = 1 - tan^2 beta / 1 + tan^2 beta

By componendo and dividendo we get

1 - tan^2 alpha/1 + tan^2 alpha = 1 + tan^2 beta - (1 - tan^2 beta) / 1 + tan^2 beta + 1 - tan^2 beta

cos2 alpha = 2 tan^2 beta / 2

tan^2 beta = cos^2 alpha - sin^2 alpha

Answer 2

Answer:

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