Question

2sin40°cos40°:cos10°

Answer 1

Ответ: 1

Пошаговое объяснение:

Answer 2

To simplify the expression 2sin(40°)cos(40°)/cos(10°), you can use trigonometric identities.

1. Start by expressing sin(2θ) in terms of trigonometric identities: sin(2θ) = 2sin(θ)cos(θ)

2. Use this identity to rewrite sin(40°)cos(40°) as sin(2 * 20°): sin(40°)cos(40°) = 2sin(20°)cos(20°)

3. Now, rewrite the expression with this substitution: 2sin(20°)cos(20°)/cos(10°)

4. To further simplify, use the double-angle identity for sine: sin(2θ) = 2sin(θ)cos(θ)

   In this case, θ = 20°, so: sin(40°) = 2sin(20°)cos(20°)

5. Substitute this back into the expression: 2(2sin(20°)cos(20°))/cos(10°)

6. Now, you have a simplified expression: 4sin(20°)cos(20°)/cos(10°)

This is the simplified form of the given expression.