Question

Show that sin(45+x) - sin(45-x) = √2 sin x

Answer 1

Answer:

$\sin \left(45^{\circ \:}+x\right)-\sin \left(45^{\circ \:}-x\right)=\sqrt{2}\sin \left(x\right)$

Step-by-step explanation:

$\sin \left(45^{\circ \:}+x\right)-\sin \left(45^{\circ \:}-x\right)$

$=\sin \left(45^{\circ \:}+x\right)-\frac{\sqrt{2}\cos \left(x\right)-\sqrt{2}\sin \left(x\right)}{2}$

$=\frac{\sqrt{2}\cos \left(x\right)+\sqrt{2}\sin \left(x\right)}{2}-\frac{\sqrt{2}\cos \left(x\right)-\sqrt{2}\sin \left(x\right)}{2}$

$=\sqrt{2}\sin \left(x\right)$

$\mathrm{ZARA}$