Question

Решите выражения (в закрепе)

Answer 1

5)

$\displaystyle 3cos(\pi +\beta )+2sin(-\frac{\pi }{2}+\beta )=-3cos\beta -2cos\beta =-5cos\beta \\\\-5*(-\frac{3}{5})=3$

6)

$\displaystyle 2sin(\alpha +\pi )+7cos(\frac{3\pi }{2}+\alpha )=-2sin\alpha +7sin\alpha =5sin\alpha \\\\5*(-0.6)=-3$

7)

$\displaystyle3sin^2\alpha +8cos^2\alpha =7(sin^2\alpha +cos^2\alpha )\\\\8cos^2a-7cos^2a=7sin^2a-3sin^2a\\\\cos^2a=4sin^2a\\\\1=4\frac{sin^2a}{cos^2a}\\\\\frac{1}{4}=tg^2a$