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uwing questionShow that tan’a - tancosquestionat tanc os B-cos’asin' a-sin'Bcos?B.cos? a cos? B.cosain |
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Answer» Step-by-step explanation: 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 |
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