Question

Помогите, пожалуйста с №1,3,4

Answer 1

1. а) $sin70^0+sin50^0=2sin frac{ 70^0 + 50^0 }{2} cos frac{70^0 - 50^0 }{2} =2sin60^0cos10^0$
б) $sin70^0-sin50^0=2sin frac{70^0-50^0}{2} cosfrac{70^0+50^0}{2}=2sin10^0cos60^0$
в) $cos70^0+cos50^0=2cos frac{70^0-50^0}{2}cos frac{70^0+50^0}{2}=2cos10^0cos60^0$
г) $cos70^0-cos50^0=-2sin frac{70^0+50^0}{2}sin frac{70^0-50^0}{2} =-2sin60^0sin10^0$
2. $sin200^0+sin100^0=sin40^0$
$sin200^0+sin100^0=2sin frac{200^0+100^0}{2} cos frac{200^0-100^0}{2}=2sin150^0cos50^0=$$2sin(180^0-30^0)cos(90^0-40^0)=2sin30^0sin40^0=2* frac{1}{2} sin40^0$$=sin40^0$
$sin40^0=sin40^0$
3.$sin frac{7 pi }{12} +sin frac{ pi }{12} +cos frac{ pi }{12} -cos frac{7 pi }{12} =2sin frac{ frac{7 pi }{12} + frac{ pi }{12} }{2} cos frac{ frac{7 pi }{12} - frac{ pi }{12} }{2} =2sin frac{ pi }{3} cos frac{ pi }{4} =$$2* frac{ sqrt{3} }{2} * frac{ sqrt{2} }{2} =frac{ sqrt{6} }{2}$
4. $sin13^0+sin15^0+sin17^0=(sin13^0+sin17^0)+sin15^0=$$2sin frac{17^0+13^0}{2}cos frac{17^0-13^0}{2} +sin15^0=2sin15^0cos2^0+sin15^0=$$sin15^0(2cos2^0+1)$