Question

Докажите тождество 1-1/cos²a=-tg²a

Answer 1

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