Question

Sin^4 15° - cos^4 15°

Answer 1

Ответ:

Пошаговое объяснение:

=(sin^2 15+cos^2 15)(sin^2 15-cos^2 15)= -1*(cos^2 15-sin^2 15)=-cos30=-V3/2

(V-корень)

Answer 2

To simplify the expression sin^4 15° - cos^4 15°, we can use the identity:

sin^2 θ - cos^2 θ = 1

Let's rewrite the expression using this identity:

(sin^2 15°)^2 - (cos^2 15°)^2

Now, let's substitute sin^2 15° and cos^2 15° with their respective values:

[(1/2)^2]^2 - [(√3/2)^2]^2

Simplifying further:

(1/4)^2 - (√3/2)^2

1/16 - 3/4

To subtract these fractions, we need a common denominator:

1/16 - 12/16 = -11/16

Therefore, sin^4 15° - cos^4 15° is equal to -11/16.