Question

Sin(2π+a)-cos(π/2+a)​

Answer 1

Ответ:

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

Answer 2

To evaluate the expression $\sin(2\pi + a) - \cos\left(\frac{\pi}{2} + a\right)$, you can use the properties of trigonometric functions and angle addition formulas.

1. $\sin(2\pi + a)$: Since $\sin(2\pi) = 0$, you have $\sin(2\pi + a) = \sin(a)$.

2. $\cos\left(\frac{\pi}{2} + a\right)$: Using the angle addition formula for cosine, you can rewrite this as: $\cos\left(\frac{\pi}{2} + a\right) = \cos\left(\frac{\pi}{2}\right) \cos(a) - \sin\left(\frac{\pi}{2}\right) \sin(a)$ $= (0) \cos(a) - (1) \sin(a)$ $= -\sin(a)$

Now, you can substitute these results back into the original expression:

$\sin(a) - (-\sin(a)) = \sin(a) + \sin(a) = 2\sin(a)$

So, the simplified expression is $2\sin(a)$.