Question

 

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((1-sina)(1+sina))-((1-2sina)cos^2a)

Answer 1

$frac{1-sin a}{1+ sin a}-frac{1-2sin a}{cos^2 a}=\ frac{(1-sin a)^2}{(1+sin a)(1-sin a)}-frac{1-2sin a}{cos^2 a}=\ frac{(1-2sin a+sin^2 a}{1-sin^2 a}-frac{1-2sin a}{cos^2 a}=\ frac{(1-2sin a+sin^2 a}{cos^2 a}-frac{1-2sin a}{cos^2 a}=\ frac{(1-2sin a+sin^2 a-(1-2sin a)}{cos^2 a}=\ frac{(1-2sin a+sin^2 a-1+2sin a)}{cos^2 a}=\ frac{sin^2 a}{cos^2 a}=tg^2 a$