Write the expression as the sine, cosine, or tangent of an angle. cos 96° cos 15° + sin 96° sin 15°
cos 81°, cos 111°, sin 111°, sin 81°

Solution:

We will use the trigonometric identity

cos (x + y) = cos x cos y + sin x sin y

We can express the given expression in terms of cos.

Using the sin cos formulas, we know that

cos(96° + 15°) = cos 96° cos 15° + sin 96° sin 15°

cos 111° = cos 96° cos 15° + sin 96° sin 15°

Also in terms of sine and tan, we express it as follows:

sin θ = cos [π/2 - θ]

sin 111° = cos [π/2 - 111°]

tan θ = sin θ/cos θ

tan 111° = cos [π/2 - 111°] / cos 111°

Write the expression as the sine, cosine, or tangent of an angle. cos 96° cos 15° + sin 96° sin 15°

Summary:

The expression cos 96° cos 15° + sin 96° sin 15° as the sine, cosine, or tangent of an angle is cos [π/2 - θ], cos 111° and cos [π/2 - 111°] / cos 111°.