Trigonometry Formulas involving Double Angle Identities

Trigonometry Formulas involving Double Angle Identities:

• sin(2x) = 2 sin(x).cos(x)
• $cos\left(2x\right)=co{s}^2\left(x\right)–si{n}^2\left(x\right),$
• $cos\left(2x\right)=2co{s}^2\left(x\right)-1$
• $cos\left(2x\right)=1–2si{n}^2\left(x\right)$
• $tan\left(2x\right)=\frac{\left[2tan\right(x\left)\right]}{[1-ta{n}^2(x\left)\right]}$

E.Trigonometry Formulas involving Half Angle Identities:

• $sin\frac{x}{2}=\pm \sqrt{\frac{1-cosx}{2}}$
• $cos\frac{x}{2}=\pm \sqrt{\frac{1+cosx}{2}}$
• $tan\left(\frac{x}{2}\right)=\sqrt{\frac{1-cos\left(x\right)}{1+cos\left(x\right)}}$

Also, $tan\left(\frac{x}{2}\right)=\sqrt{\frac{1-cos\left(x\right)}{1+cos\left(x\right)}}=\sqrt{\frac{(1-cos(x\left)\right)(1-cos(x\left)\right)}{(1+cos(x\left)\right)(1-cos(x\left)\right)}}=\sqrt{\frac{(1-cos(x){)}^2}{1-co{s}^2\left(x\right)}}=\sqrt{\frac{(1-cos(x){)}^2}{si{n}^2\left(x\right)}}=\frac{1-cos\left(x\right)}{sin\left(x\right)}$

So, $tan\left(\frac{x}{2}\right)=\frac{1-cos\left(x\right)}{sin\left(x\right)}$