Power reduction Identities

Power Reducing in terms of Double angle

$(1) \,\,\,\,\,\,$ $\sin^2{\theta} \,=\, \dfrac{1-\cos{2\theta}}{2}$

$(2) \,\,\,\,\,\,$ $\cos^2{\theta} \,=\, \dfrac{1+\cos{2\theta}}{2}$

$(3) \,\,\,\,\,\,$ $\tan^2{\theta} \,=\, \dfrac{1-\cos{2\theta}}{1+\cos{2\theta}}$

$(4) \,\,\,\,\,\,$ $\cot^2{\theta} \,=\, \dfrac{1+\cos{2\theta}}{1-\cos{2\theta}}$

$(5) \,\,\,\,\,\,$ $\sec^2{\theta} \,=\, \dfrac{2}{1+\cos{2\theta}}$

$(6) \,\,\,\,\,\,$ $\csc^2{\theta} \,=\, \dfrac{2}{1-\cos{2\theta}}$

Power Reducing in terms of an angle

$(1) \,\,\,\,\,\,$ $\sin^2{\Big(\dfrac{\theta}{2}\Big)} \,=\, \dfrac{1-\cos{\theta}}{2}$

$(2) \,\,\,\,\,\,$ $\cos^2{\Big(\dfrac{\theta}{2}\Big)} \,=\, \dfrac{1+\cos{\theta}}{2}$

$(3) \,\,\,\,\,\,$ $\tan^2{\Big(\dfrac{\theta}{2}\Big)} \,=\, \dfrac{1-\cos{\theta}}{1+\cos{\theta}}$

$(4) \,\,\,\,\,\,$ $\cot^2{\Big(\dfrac{\theta}{2}\Big)} \,=\, \dfrac{1+\cos{\theta}}{1-\cos{\theta}}$

$(5) \,\,\,\,\,\,$ $\sec^2{\Big(\dfrac{\theta}{2}\Big)} \,=\, \dfrac{2}{1+\cos{\theta}}$

$(6) \,\,\,\,\,\,$ $\csc^2{\Big(\dfrac{\theta}{2}\Big)} \,=\, \dfrac{2}{1-\cos{\theta}}$