Question

Помогите сделать три номера 78;80;82 пожалуйста ​

Answer 1

$78.\ \ \ sin\beta \cdot cos\beta =0,4\\\\sin^4\beta +cos^4\beta =(\underbrace {sin^2\beta +cos^2\beta }_{1})^2-2sin^2\beta \cdot cos^2\beta =1-2(sin\beta \cdot cos\beta )^2=\\\\=1-2\cdot 0,4^2=1-0,32=\boxed {\ 0,68\ }$

$80.\ \ \ cos2\varphi =0,7\\\\sin^4\varphi -cos^4\varphi =(sin^2\varphi -cos^2\varphi )(\underbrace {sin^2\varphi +cos^2\varphi }_{1})=-(\underbrace {cos^2\varphi -sin^2\varphi }_{cos2\varphi })\cdot 1=\\\\=-cos2\varphi =\boxed {\ -0,7\ }$

$82.\ \ \ cos2\beta =-0,8\\\\cos2\beta =\dfrac{1-tg^2\beta }{1+tg^2\beta }\ \ \Rightarrow \ \ \ cos2\beta +cos2\beta \cdot tg^2\beta =1-tg^2\beta \ ,\\\\cos2\beta \cdot tg^2\beta +tg^2\beta =1-cos2\beta \\\\tg^2\beta \cdot (cos2\beta +1)=1-cos2\beta \ \ ,\ \ \ tg^2\beta =\dfrac{1-cos2\beta }{1+cos2\beta }\ ,\\\\tg^2\beta =\dfrac{1+0,8}{1-0,8}=\dfrac{1,8}{0,2}=9\ \ \ \Rightarrow \ \ \ tg\beta =\pm 3\\\\\\\dfrac{\pi}{2}<\beta <\pi \ \ \Rightarrow \ \ \ tg\beta <0\ \ \ \Rightarrow \ \ \ \boxed{\ tg\beta =-3\ }$