Question

2sin35 *cos10 - sin25 упростите выражение

Answer 1

Ответ:

=2sin2acosa\-2sin2asina=-cosa/sina=-tga

Пошаговое объяснение:

Answer 2

To simplify the expression, we'll first convert the angles from degrees to radians and then use trigonometric identities to simplify the expression:

1. Convert the angles to radians: 35 degrees = 35 * π / 180 radians 10 degrees = 10 * π / 180 radians 25 degrees = 25 * π / 180 radians

2. Use trigonometric identities: sin(a) * cos(b) = (1/2) * [sin(a + b) + sin(a - b)]

Now, let's simplify the expression step by step:

Expression: 2sin35 * cos10 - sin25

Step 1: Convert angles to radians sin(35°) = sin(35 * π / 180) ≈ 0.57357643635 cos(10°) = cos(10 * π / 180) ≈ 0.98480775301 sin(25°) = sin(25 * π / 180) ≈ 0.42261826174

Step 2: Use the trigonometric identity for sin(a) * cos(b) 2 * [(1/2) * (sin(35 + 10) + sin(35 - 10))] - sin(25)

Step 3: Simplify the expressions inside the brackets 2 * [(1/2) * (sin(45) + sin(25))] - sin(25)

Step 4: Use the value of sin(45°) and sin(25°) (both are equal to √2/2) 2 * [(1/2) * (√2/2 + √2/2)] - √2/2

Step 5: Simplify further 2 * [1/2 * (√2)] - √2/2

Step 6: Evaluate the expression 2 * (√2/2) - √2/2 √2 - √2/2

Step 7: Combine like terms (√2 - 1) * √2 / 2

The final simplified expression is (√2 - 1) * √2 / 2.