Question

упростите выражение (tg^2-sin^2a)(1/sin^2a-1)

Answer 1

$(tg^2a-sin^2a) \dfrac{1}{sin^2a-1}= \\ \\ =( \dfrac{sin^2a}{cos^2a}-sin^2a) \dfrac{1}{-cos^2a} = \\ \\ = -\dfrac{1}{cos^2a}* \dfrac{sin^2a-sin^2acos^2a}{cos^2a}= \\ \\ = -\dfrac{1}{cos^2a}* \dfrac{sin^2a(1-cos^2a)}{cos^2a}= \\ \\ = -\dfrac{sin^4a}{cos^4a}=-tg^4a$