Find the exact value of the given expression using a sum or difference formula.

Question

Quizplus · Accepted Answer

Without knowing the specific formula, we see that the given expression involves the difference of two angles. This suggests that we use the formula for the sine of a difference, which is:

sin(x - y) = sin x cos y - cos x sin y

In this case, we have:

sin(75° - 15°) = sin 75° cos 15° - cos 75° sin 15°

We can use the fact that sin(75°) = cos(15°) and cos(75°) = sin(15°) to simplify this to:

sin(75° - 15°) = sin 75° cos 15° - cos 75° sin 15°
= cos 15° cos 15° - sin 15° sin 15°
= cos^2 15° - sin^2 15°

Using the identity cos^2 x - sin^2 x = cos 2x, we find that:

cos^2 15° - sin^2 15° = cos 30° = √3 / 2

Therefore, the answer is D) 11eb80b1_afb0_d3a0_a291_b7c2d07ef452_TB8633_11.

Find the Exact Value of the Given Expression Using a Sum