Question

Write the expression as the sine, cosine, or tangent of an angle. cos 112° cos 45° + sin 112° sin 45°

Answer 1

The answer is cos 67°.

Answer 2

cos 112° cos 45° + sin 112° sin 45° = cos(67)°

Explanation:

Given trigonometric expression

cos 112° cos 45° + sin 112° sin 45°

We know, the trigonometric identity

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

On comparing cos 112° cos 45° + sin 112° sin 45° and cos A cos B + sin A sin B, we can see that A= 112° and B = 45°.

Plugging value A= 112° and B = 45° in cos (A-B), we get

cos ( 112- 45) = cos(67)°

Therefore, cos 112° cos 45° + sin 112° sin 45° = cos(67)°