Question

Помогите решить пример 1/cos^a- tg^2 a (cos^2 a + 1)

Answer 1

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