Question

verify the identity. sin(pi/2 + x)=cos x

Answer 1

you can use the "addition angle formula"
\[\sin(\alpha +\beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)\]
with \(\alpha =\frac{\pi}{2}\) and \(\beta=x\)

Answer 2

also you need to know that \(\sin(\frac{\pi}{2})=1\) and \(\cos(\frac{\pi}{2})=0\)

Answer 3

what about find all solutions of the equation in the interval (0,2pi). sin(x + pi/6) - sin(x - pi/6)= 1/2