Question

Sin (-a) - sin a * ctg^2 (-a) = ?

Answer 1

Решение-во вложении                                             

Answer 2

///////////////////////////////////////////////////////

Answer 3

Calculation of the Expression

To calculate the expression sin(-a) - sin(a) * ctg^2(-a), we can break it down into smaller steps using trigonometric identities.

1. First, let's rewrite the expression using the definitions of cotangent (ctg) and tangent (tg): sin(-a) - sin(a) * (1 / tan^2(-a))

2. Next, we can simplify the expression by using the identities: - sin(-a) = -sin(a) (the sine function is an odd function) - tan(-a) = -tan(a) (the tangent function is an odd function)

Applying these identities, the expression becomes: -sin(a) - sin(a) * (1 / (-tan(a))^2)

3. Simplifying further, we can rewrite the expression as: -sin(a) - sin(a) * (1 / tan^2(a))

4. Finally, we can factor out -sin(a) from both terms: -sin(a) * (1 + 1 / tan^2(a))

Therefore, the simplified expression is -sin(a) * (1 + 1 / tan^2(a)).

Please note that this answer is based on the trigonometric identities and simplifications. If you have a specific value for a, you can substitute it into the expression to get a numerical result.

Let me know if you have any further questions!