Question

What is the value of cos 70° cos 40° + sin 70° sin 40°?

Answer 1

Apply the trig identity: sin (a - b) = sin a.cos b - sin b.cos a
sin 70.cos 40 - sin 40.cos 70 = sin (70 - 40) =
(sin30)

Answer 2

The value of (cos 70° cos 40° + sin 70° sin 40°) is ✓3/2.

Here we have to apply the compound angle formula of (cos A cos B + Sin A Sin B) = cos (A-B)

Here,

A = 70°

B = 40°

Applying the formula,

cos 70° cos 40° + sin 70° sin 40° = cos (70°-40°) = cos 30° = ✓3/2 (answer)