Find the value of $\sin 3°$.

If $\sin A+\sin B=a$ and $\cos A+\cos B=b$, show that $\tan \left(A+B\right)=\frac{2ab}{b^2-a^2}$

If $\sin A+\sin B=a$ and $\cos A+\cos B=b$, show that $\sin \left(A+B\right)=\frac{2ab}{b^2+a^2}$

If $\sin A+\sin B=a$ and $\cos A+\cos B=b$, show that $\cos \left(A+B\right)=\frac{b^2-a^2}{b^2+a^2}$

Prove the following:

$\frac{1+\sin A-\cos A}{1+\sin A+\cos A}=\tan \frac{A}{2}$

Prove: $8{\sin }^4\frac{1}{2}\theta -8{\sin }^2\frac{1}{2}\theta +1=\cos 2\theta$

Prove: ${\cos }^4\frac{\pi }{8}+{\cos }^4\frac{3\pi }{8}+{\cos }^4\frac{5\pi }{8}+{\cos }^4\frac{7\pi }{8}=\frac{3}{2}$