$$\sin\left(a+b\right)=\sin a.\cos b+\cos a.\sin b$$

$$\sin\left(a-b\right)=\sin a.\cos b-\cos a.\sin b$$

$$\cos2a=1-2\sin^2a$$

$$\frac{\sqrt{6}+\sqrt{2}}{4}$$  

$$\frac{\sqrt{6}-\sqrt{2}}{4}$$  

$$-\frac{\sqrt{6}+\sqrt{2}}{4}$$  

$$\frac{\sqrt{2}-\sqrt{6}}{4}$$  

$$-\frac{1}{7}$$  

$$-7$$  

$$\frac{1}{7}$$  

$$7$$   

$$\cos^2x=\frac{1+\cos2x}{2}$$  

$$\cos2x=1-2\sin^2x$$  

$$\sin2x=2.\sin x.\cos x$$  

$$\sin^2x=-\frac{1+\cos2x}{2}$$  

$$\cos2a=\sin^2a-\cos^2a$$

$$\cos2a=1-2\cos^2a$$

$$\cos2a=2\sin^2a-1$$

$$\frac{3}{4}$$  

$$-\frac{3}{8}$$  

$$\frac{\sqrt{2}}{2}$$  

$$-\frac{3}{4}$$  

$$\cos a-\cos b=-2.\sin\frac{a+b}{2}.\sin\frac{a-b}{2}$$

$$\sin a-\sin b=-2.\cos\frac{a+b}{2}.\sin\frac{a-b}{2}$$

$$\sin a+\sin b=2.\sin\frac{a+b}{2}.\cos\frac{a-b}{2}$$

$$\frac{1}{2}$$  

$$-\frac{1}{2}$$  

$$\frac{1}{4}$$  

$$-\frac{1}{4}$$  

$$\frac{1}{16}$$  

$$\frac{1}{8}$$  

$$\frac{3}{16}$$  

$$\frac{1}{4}$$