Question

Помогите пожалуйста!!!! Вычислите:$Cos \pi - Sin( -\frac{5 \pi }{2})+tg^2 * \frac{4 \pi }{3}$

Answer 1

$\mathtt{cos\pi-sin(-\frac{5\pi}{2})+tg^2(\frac{4\pi}{3})=cos\pi+sin(2\pi+\frac{\pi}{2})+tg^2(\pi+\frac{\pi}{3})=}\\\mathtt{cos\pi+sin(\frac{\pi}{2})+tg^2(\frac{\pi}{3})=-1+1+(\frac{sin(\frac{\pi}{3})}{cos(\frac{\pi}{3})})^2=(sin(\frac{\pi}{3}):cos(\frac{\pi}{3}))^2=}\\\mathtt{(\frac{1}{2}:\frac{\sqrt{3}}{2})^2=[(\sqrt{3}})^{-1}]^2=(\sqrt{3}})^{-2}=\frac{1}{3}}$