When
tan= a 12/5
than evaluate cos2a

The value of Cos 2a is - ( ) .

Step-by-step explanation:

Given as

Tan a =

Now, ∵  Tan Ф =  

So,  Tan a =

Or, =

Or, From Pythagoras Theorem

Hypotenuse² = perpendicular² + Base²

Or, Hypotenuse² = 12² + 5²

Or, Hypotenuse² = 144 + 25

Or, Hypotenuse² = 169

∴ Hypotenuse = = 13

Take Hypotenuse = 13

Now,∵ Cos 2Ф = Cos²Ф - Sin²Ф

So, Cos 2a = Cos²a - Sin²a

or ,  Cos 2a = 1 - 2 Sin²a                               ∵ Cos²a + Sin²a = 1

Or, Cos 2a = 1 - 2 ×( )²

Or ,  Cos 2a = 1 - 2 ×( )²

Or, Cos 2a = 1 - 2 × ()

Or, Cos 2a = ()

∴  Cos 2a = - ()

Hence the value of Cos 2a is - ()  . answer