Question

Write the expression as the sine or cosine of an angle sin(pi/7) cos(x) + cos(pi/7) sin(x)

Answer 1

Answer:

$\sin(\frac{\pi}{7}+x)$

Step-by-step explanation:

We are going to use the identity

$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$

because this identities right hand side matches your expression where

$a=\frac{\pi}{7}$ and $b=x$.

So we have that $\sin(\frac{\pi}{7})\cos(x)+\cos(\frac{\pi}{7})\sin(x)$ is equal to $\sin(\frac{\pi}{7}+x)$.