Question

Show that $cos2A=co{s}^{4}A-si{n}^{4}A$

Answer 1

${\cos }^{2}A={\cos }^{4}A-{\sin }^{4}A$

$\text{R}\text{H}\text{S}$

${\cos }^{4}A-{\sin }^{4}A$

$=({\cos }^{2}A-{\sin }^{2}A)({\cos }^{2}A+{\sin }^{2}A)$

$=\left({\cos }^{2}A\right)\left(1\right)$

$={\cos }^{2}A$ (proved)

Hence $LHS=RHS$