Question

prove that cos340°*cos40°+sin200°*sin140°=1/2​

Answer 1

Explanation:

Cos 340 * cos 40 + sin 200 * sin 140

cos(360-20)*cos40+sin(180+20)*sin(180-40)

cos20*cos40+(-sin20)*sin40

cos20*cos40-sin20*sin40

cos A * cos B - sin A * sin B = cos(A+B)

so, cos(40+20)= cos60 = 0.5