Question

Sin(П/2-x)*tg(-x)/cos(П/2+x)

Answer 1

$\cos(x) \times - \frac{ \sin(x) }{ \cos(x) } \div ( - sinx) = 1$

Answer 2

Let's simplify the expression step by step:

1. Recall the trigonometric identities:

• sin(π/2 - x) = cos(x)
• tan(-x) = -tan(x)
• cos(π/2 + x) = sin(x)

2. Replace the trigonometric functions in the expression:

sin(π/2 - x) * tan(-x) / cos(π/2 + x) = cos(x) * (-tan(x)) / sin(x)

3. Cancel out common factors:

cos(x) and sin(x) are common factors, so they cancel out:

(-tan(x))

So, the simplified expression is: -tan(x)