Question

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

Answer 1

Используем "Формулы приведения". Решение на фото

Answer 2

To simplify the given expression, let's break it down step by step:

1. Recall the trigonometric identities:

• sin(π/2 - α) = cos(α)
• cos(π - α) = -cos(α)
• tan(π - α) = -tan(α)
• cot(3π/2 + α) = -cot(α)

2. Substitute these identities into the given expression:

sin(π/2 - α) - cos(π - α) + tan(π - α) - cot(3π/2 + α) = cos(α) - (-cos(α)) + (-tan(α)) - (-cot(α)) = cos(α) + cos(α) - tan(α) + cot(α) = 2cos(α) - tan(α) + cot(α)

And that's the simplified form of the expression: 2cos(α) - tan(α) + cot(α).