Question

(1+tg²альфа)cos²альфа-1​

Answer 1

$(1 + \text{tg}^{2} \, \alpha )\cos^{2}\alpha - 1 = \dfrac{1}{\cos^{2}\alpha } \cdot \cos^{2}\alpha - 1 = 1 - 1 = 0$

Answer 2

Let's simplify the expression step by step:

1. We know that the trigonometric identity for tangent squared is: tan²(α) = sec²(α) - 1

2. Therefore, we can substitute tan²(α) in the expression: 1 + tan²(α) = 1 + (sec²(α) - 1) = sec²(α)

3. Now, we have the expression: (1 + tan²(α)) * cos²(α) - 1

4. Substituting sec²(α) from step 2: sec²(α) * cos²(α) - 1

5. Using the identity sec²(α) = 1/cos²(α): (1/cos²(α)) * cos²(α) - 1

6. The cos²(α) terms cancel out, and we get: 1 - 1 = 0

So, the simplified expression is 0.