Question

1) вычислить:


2) :





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Answer 1

$1)36\sqrt{3}*tg\frac{\pi }{3}*Sin\frac{\pi }{6}=36\sqrt{3}*\sqrt{3}*\frac{1}{2}=36*3*\frac{1}{2}=54\\\\2)54\sqrt{3}*tg\frac{\pi }{6}*Sin\frac{\pi }{6}=54\sqrt{3}*\frac{1}{\sqrt{3}}*\frac{1}{2}=54*\frac{1}{2}=27$

$3)Cos^{2}(2\pi-t)+Cos^{2}(\frac{3\pi }{2}+t)=Cos^{2}t+Sin^{2}t=1\\\\4)\frac{1-Cos^{2}\alpha}{Sin^{2}\alpha} =\frac{Sin^{2}\alpha}{Sin^{2}\alpha}=1$

$5)Sin^{2}(\pi+t)+Sin^{2}(\frac{\pi }{2}+t)=Sin^{2}t+Cos^{2}t=1\\\\6)\frac{1-Sin^{2}\alpha}{Cos^{2}\alpha}=\frac{Cos^{2}\alpha}{Cos^{2} \alpha}=1$