tga=2 , tg(a+β)=4tg(a+β)=1−tga⋅tgβtga+tgβ , 1−2tgβ2+tgβ=4 , 2+tgβ=4−8tgβ ,9tgβ=2 , tgβ=92
\begin{gathered}2)\ \ tg(\dfrac{3\pi}{2}-x)=\dfrac{tg\frac{3\pi}{2}-tgx}{1-tg\frac{3\pi}{2}\cdot tgx}y=tgx\ \ \to \ \ \ OOF:\ \ x\ne \dfrac{\pi}{2}+\pi n\ ,\ n\in Z\ \ \Rightarrow \ \ tg\dfrac{3\pi}{2}\ ne\ syshestvyet\end{gathered}2) tg(23π−x)=1−tg23π⋅tgxtg23π−tgxy=tgx → OOF: x=2π+πn , n∈Z ⇒ tg23π ne syshestvyet
По формулам приведения: tg(\dfrac{3\pi}{2}-x)=tgxtg(23π−x)=tgx
\begin{gathered}3)\ \ cosx=\dfrac{11}{13}x\in (\dfrac{3\pi}{2}\, ;\, 2\pi \, )\ \ \ \to \ \ \ 2x\in (\, 3\pi \ ;\ 4\pi \ )cos2x-4,8=(2cos^2x-1)-4,8=2\cdot \dfrac{121}{169}-4,8=\dfrac{-569,2}{169}=-3,368\end{gathered}3) cosx=1311x∈(23π;2π) → 2x∈(3π ; 4π )cos2x−4,8=(2cos2x−1)−4,8=2⋅169121−4,8=169−569,2=−3,368
