Question

Sin(П/2-а)-sin(П-а)-cos(П-а)-sin(2П-а)

Answer 1

$Sin( \frac{ \pi }{2}- \alpha )-Sin( \pi - \alpha )-Cos( \pi - \alpha )-Sin(2 \pi - \alpha )=Cos \alpha -Sin \alpha$ $+Cos \alpha +Sin \alpha =2Cos \alpha$

Answer 2

$sin( \frac{\pi}{2}-\alpha)-sin( \pi-\alpha)-cos(\pi-\alpha)-sin(2\pi-\alpha) \\ \\ cos(\alpha)-sin(\alpha)-(-cos(\alpha))-(-sin(\alpha)) \\ \\ cos(\alpha)-sin(\alpha)+cos(\alpha)+sin(\alpha) =2cos(\alpha)$

Answer 3

Let's simplify the expression:

sin(π/2 - a) - sin(π - a) - cos(π - a) - sin(2π - a)

1. sin(π/2 - a) can be simplified using the angle difference identity for sine: sin(π/2 - a) = sin(π/2)cos(a) - cos(π/2)sin(a) Since sin(π/2) = 1 and cos(π/2) = 0: sin(π/2 - a) = 1 * cos(a) - 0 * sin(a) = cos(a)

2. sin(π - a) can be simplified using the angle difference identity for sine: sin(π - a) = sin(π)cos(a) - cos(π)sin(a) Since sin(π) = 0 and cos(π) = -1: sin(π - a) = 0 * cos(a) - (-1) * sin(a) = sin(a)

3. cos(π - a) can be simplified similarly: cos(π - a) = cos(π)cos(a) + sin(π)sin(a) Since cos(π) = -1 and sin(π) = 0: cos(π - a) = (-1) * cos(a) + 0 * sin(a) = -cos(a)

4. sin(2π - a) can also be simplified: sin(2π - a) = sin(2π)cos(a) - cos(2π)sin(a) Since sin(2π) = 0 and cos(2π) = 1: sin(2π - a) = 0 * cos(a) - 1 * sin(a) = -sin(a)

Now, substitute these simplified expressions back into the original equation:

cos(a) - sin(a) - (-cos(a)) - (-sin(a))

Simplify further:

cos(a) - sin(a) + cos(a) + sin(a)

Now, combine like terms:

2cos(a)

So, the simplified expression is 2cos(a).