Question

Упростите выражение!!!плз

Answer 1

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

Answer 2

(а+в)*(а-в)=а²-в²;
1/cos²β - tg²β=1/cos²β - sin²β/cos²β=(1-sin²β)/cos²β=cos²β/cos²β=1/