Solution assignment 05 Addition and subtraction formulas

Show the following relation using some trigonometric formulas:

$\sin(\displaystyle\frac{\pi}{2}-x)=\cos(x)$

We can derive this formula from the unit circle, see also Trigonometry Unit circle and simple formulas. Now we use the following formula for the left-hand side:

$\sin(\displaystyle\frac{\pi}{2}-x)=\sin(\displaystyle\frac{\pi}{2})\cos(x)-\sin(x)\cos(\displaystyle\frac{\pi}{2})=$

$=1.\cos(x)-\sin(x).0=\cos(x)$