Question

Вычислите: cos*p/2-sin*3p/2

Answer 1

$Cos\frac{\pi }{2}-Sin\frac{3\pi }{2}=0-(-1) =0+1=1$

Answer 2

To calculate the expression cos(p/2) - sin(3p/2), we'll use trigonometric identities. Remember that cos(x - π/2) = sin(x) and sin(x + π/2) = cos(x). So, we can rewrite the expression as follows:

cos(p/2) - sin(3p/2) = cos(p/2) - sin(p/2 + π)

Now, let's use the addition formula for sine: sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

sin(p/2 + π) = sin(p/2)cos(π) + cos(p/2)sin(π)

Remember that sin(π) = 0 and cos(π) = -1, so:

sin(p/2 + π) = sin(p/2)(0) + cos(p/2)(-1)

sin(p/2 + π) = -cos(p/2)

Now, the expression becomes:

cos(p/2) - sin(3p/2) = cos(p/2) - (-cos(p/2))

cos(p/2) + cos(p/2) = 2cos(p/2)

So, the final answer is 2cos(p/2).