Periodicity Identities - radians:
\[sin(x + 2\pi )=sin x \] \[cos(x + 2\pi )=cos x \]
\[tan(x + 2\pi )=tanx \] \[cot(x + 2\pi )=cotx \]
Periodicity Identities - degrees:
\[sin(x + 360^{\circ})=sinx \] \[cos(x + 360^{\circ})=cosx \]
\[tan(x + 360^{\circ})=tanx \] \[cot(x + 360^{\circ})=cotx \]
Sum/Difference Identities:
\[sin(x+y) = sin(x)cos(y) + sin(y)cos(x) \]
\[cos(x+y) = cos(x)cos(y) - sin(x)sin(y) \]
\[tan(x+y) = \frac{tan(x)+tan(y)}{1-tan(x).tan(y)} \]
\[sin(x-y) = sin(x)cos(y)-cos(x)sin(y) \]
\[cos(x-y) = cos(x)cos(y) + sin(x)sin(y) \]
\[tan(x-y) = \frac{tan(x) -tan(y) }{1 + tan(x)tan(y)} \]
Double Angle Identities:
\[sin(2x)=2sin(x)cos(x) \]
\[cos(2x)=cos2(x) - sin2(x) \]
\[cos(2x)=2cos2(x) - 1 \]
\[cos(2x)=1-2sin2(x) \]
\[tan(2x)=\frac{2tan(x)}{1-tan2(x)} \]
Half Angle Identities:
\[sin\left (\frac{\pi }{2} \right ) = \pm \sqrt{\frac{1-cos x}{2}}\]
\[cos\left (\frac{\pi }{2} \right ) = \pm \sqrt{\frac{1+cos x}{2}} \]
\[cos\left (\frac{\pi }{2} \right ) = \pm \sqrt{\frac{1-cos x}{1+cos x}} \]
Sum to Product Identities:
\[sin \: x + sin\: y = 2sin\frac{x+y}{2}cos\frac{x-y}{2} \]
\[sin \: x - sin\: y = 2cos\frac{x+y}{2}sin\frac{x-y}{2} \]
\[cos \: x + cos\: y = 2cos\frac{x+y}{2}cos\frac{x-y}{2} \]
cos \: x - cos\: y = 2sin\frac{x+y}{2}sin\frac{x-y}{2}
Product identities:
\[sin\: x.cos\: y= \frac{sin(x+y)+sin(x-y)}{2} \]
\[ cos\: x.cos\: y= \frac{cos(x+y)+cos(x-y)}{2} \]
\[sin\: x.sin\: y= \frac{cos(x+y)-cos(x-y)}{2} \]
