Question

Sin(П/2 + альфа) + cos(П + альфа) + ctg(2П - альфа) + tg(3П/2 - альфа)

Answer 1

Формулы приведения в помощь.

Answer 2

=sin (π/2 + альфа)-cos (альфа)-ctg(альфа)+tag(3π/2-альфа)=cos(альфа)-cos(альфа)-ctg(альфа)+ctg(альфа)=0

Ответ: 0

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Answer 3

To simplify the given expression, let's evaluate each trigonometric term step by step:

1. Sin(π/2 + α): Using the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we can rewrite it as sin(π/2)cos(α) + cos(π/2)sin(α). Since sin(π/2) equals 1 and cos(π/2) equals 0, the expression simplifies to cos(α).

2. Cos(π + α): Using the identity cos(a + b) = cos(a)cos(b) - sin(a)sin(b), we can rewrite it as cos(π)cos(α) - sin(π)sin(α). Since cos(π) equals -1 and sin(π) equals 0, the expression simplifies to -cos(α).

3. Ctg(2π - α): Cotangent (ctg) is the reciprocal of tangent (tan). We can rewrite it as 1/tan(2π - α). Since tan(a + π) = -tan(a), we have tan(2π - α) = tan(-α). Therefore, ctg(2π - α) simplifies to 1/tan(-α) = -cot(α).

4. Tan(3π/2 - α): Using the identity tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b)), we can rewrite it as (tan(3π/2) - tan(α))/(1 + tan(3π/2)tan(α)). Since tan(3π/2) equals undefined, we have an indeterminate form. Therefore, the expression remains as tan(3π/2 - α).

Combining all the simplified terms, we have: cos(α) - cos(α) - cot(α) + tan(3π/2 - α).

Please note that if you have specific values for α, you can substitute them in the expression to further simplify the equation.