Question

А)cos(90°+α)-sin(180°+α)+ctg(270°+α)+tg(360°+α)

Answer 1

конечный ответ 0

все решение на картинке.

Answer 2

Let's simplify the expression step by step:

1. cos(90° + α): The cosine of the angle (90° + α) is equal to the sine of α. So, cos(90° + α) = sin(α).

2. sin(180° + α): The sine of the angle (180° + α) is equal to the sine of α, but with the opposite sign. So, sin(180° + α) = -sin(α).

3. ctg(270° + α): The cotangent of the angle (270° + α) is equal to the tangent of the angle α. So, ctg(270° + α) = tan(α).

4. tg(360° + α): The tangent of the angle (360° + α) is equal to the tangent of α. So, tg(360° + α) = tan(α).

Now, let's substitute these simplifications back into the original expression:

sin(α) - sin(α) + tan(α) + tan(α)

Since the -sin(α) and sin(α) terms cancel each other out, and the tan(α) and tan(α) terms can be combined, the expression simplifies to:

2tan(α)

Therefore, the simplified expression is 2tan(α).