Question

1)cosa*cos3a-sina*sin3a 2) sin2a*cosa+cos2a*sina 3) sin40*cos5+cos40*sin5 4) (tg7П/15-tg2П/15)/1+tg7П/15*tg2П/15 5) sina=4/5;П<a<3П/2; cosa-?

Answer 1

1) cos a cos 3a - sin a sin 3a = cos (a+3a) = cos 4a

2) sin 2a cos a + cos 2a sin a = sin (2a+a) = sin 3a

3) sin40°cos5°+cos40°sin5° = sin(40°+5°)= sin 45° = $\frac{\sqrt{2}}{2}$

4) $\dfrac{tg\frac{7\pi}{15}-tg\frac{2\pi}{15}}{1+tg\frac{7\pi}{15}tg\frac{2\pi}{15}} = tg(\frac{7\pi}{15}-\frac{2\pi}{15}) =tg\frac{5\pi}{15}=tg\frac{\pi}{3}=\sqrt{3}$

5) $\pi <\alpha <\frac{3\pi}{2} => cos \alpha <0$

$sin^2\alpha +cos^2\alpha =1\\ cos\alpha =-\sqrt{1-(\frac{4}{5})^2} =-\sqrt{1-\frac{16}{25}}=-\sqrt{\frac{9}{25}}=-\frac{3}{5}$