Question

Алгебра сделайте любое задание

Answer 1

$2)\ \ cos960^\circ =cos2\cdot 360^\circ +240^\circ )=cos240^\circ =cos(180^\circ +60^\circ )=\\\\=-cos60^\circ =-\dfrac{1}{2}\\\\\\tg\Big(-\dfrac{21\pi }{4}\Big)=-tg\dfrac{20\pi +\pi }{4}=-tg\Big(\pi +\dfrac{\pi}{4}\Big)=-tg\dfrac{\pi}{4}=-1$

$5)\ \ sin75^\circ +cos75^\circ =sin75^\circ +cos(90^\circ -15^\circ )=sin75^\circ +sin15^\circ =\\\\=2\cdot sin\dfrac{75^\circ +15^\circ }{2}\cdot cos\dfrac{75^\circ -15^\circ }{2}=2\cdot sin45^\circ \cdot cos30^\circ =2\cdot \dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}=\dfrac{\sqrt6}{2}=\dfrac{\sqrt3}{\sqrt2}$

$6)\ \ \dfrac{sin2a}{2sin^2a}=\dfrac{2\, sina\cdot cosa}{2\, sin^2a}=\dfrac{cosa}{sina}=ctga\\\\\\7)\ \ \dfrac{cos2a+1}{cos^2a}=\dfrac{2cos^2a}{cos^2a}=2\\\\\\\star\ \ cos^2a=\dfrac{1+cos2a}{2}\ \ \ \to \ \ \ 1+cos2a=2cos^2a\ \ \star$