Question

cos 340 .cos 40 + sin 200.sin140

Answer 1

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

Answer 2

Answer:

1/2 or 0.5

Step-by-step explanation:

cos 340 . cos 40 + sin 200 . sin 140

[since,

cos 340= cos (360-20) = cos20

sin 200 = sin (180+20) = -sin20

sin 140 = sin (180-40) = sin40]

= cos (360-20) . cos 40 + sin (180+20) . sin (180-40)

= cos 20 . cos 40 + (-sin 20) . sin 40

= cos 20 . cos 40 - sin 20 . sin 40

[ since, cos (A+B) = cos A . cos B - sin A . sin B ]

= cos (20+40)

= cos 60

= 1/2 or 0.5