Question

Verifique que sec² x= 1+ tg² x para todo x tal que cos x diferente de 0.

Answer 1

$\sec^2x=1+\tan^2x\\\\\frac{1}{cos^2x}=1+\frac{\sin^2x}{\cos^2x}\\\\\frac{1}{cos^2x/1}=\frac{1}{1/\cos^2x}+\frac{\sin^2x}{\cos^2x/1}\\\\1=\underbrace{\cos^2x+\sin^2x}_{1}\\\\\boxed{1=1}$

Cqd.