Question

Sin^2(25°)+cos^2(25°)-sin(15°)*cos(15°)

Answer 1

на фото.....................

Answer 2

The expression simplifies to:

sin^2(25°) + cos^2(25°) - sin(15°) * cos(15°)

Since sin^2(θ) + cos^2(θ) equals 1 for any angle θ, we can replace the first two terms with 1:

1 - sin(15°) * cos(15°)

Further simplification requires the use of trigonometric identities, such as the double-angle identity for sine:

sin(2θ) = 2 * sin(θ) * cos(θ)

Applying this identity to our expression:

1 - (1/2) * sin(30°)

Using the trigonometric value of sin(30°) = 1/2, we can substitute it in:

1 - (1/2) * (1/2)

Simplifying the expression:

1 - 1/4

The final result is:

3/4