If $$\tan \theta = \frac{3}{4}{\text{,}}$$   find the value of $${\text{cos2}}\theta $$  ?

Solution (By Examveda Team)

$$\eqalign{ & \tan \theta = \frac{3}{4} \cr & {\text{cos2}}\theta = \frac{{1 - {\text{ta}}{{\text{n}}^2}\theta }}{{1 + {\text{ta}}{{\text{n}}^2}\theta }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1 - \frac{9}{{16}}}}{{1 + \frac{9}{{16}}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{\frac{7}{{16}}}}{{\frac{{25}}{{16}}}} \cr & {\text{cos2}}\theta = \frac{7}{{25}} \cr} $$