Question

Упростить выражение:

1) $frac{1}{cos^2a} -tg^2a-sin^2a$

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

3) $frac{sina}{1+cosa} + frac{sina}{1-cosa}$

Answer 1

1) $frac{1}{Cos^{2} alpha } - frac{Sin^{2} alpha}{Cos^{2} alpha}- frac{Sin^{2} alpha*Cos^{2} alpha }{Cos^{2} alpha }= frac{Cos^{2} alpha(1-Sin^{2} alpha ) }{Cos^{2} alpha} =Cos^{2} alpha$

2) $frac{1-Sin^{2} alpha*Cos^{2} alpha -Sin^{2} alpha}{Cos^{2} alpha} =frac{Cos^{2} alpha(1-Sin^{2} alpha ) }{Cos^{2} alpha}=Cos^{2} alpha$

3) $frac{Sin alpha -Sin alpha *Cos alpha+Sin alpha +Sin alpha *Cos alpha }{1-Cos^{2} alpha } = frac{2Sin alpha }{Sin^{2} alpha } = frac{2}{Sin alpha }$