Question

Whentan= a 12/5 than evaluate cos2a​

Answer 1

Answer:

The value of Cos 2a is - ($\frac{119}{169}$ ) .

Step-by-step explanation:

Given as

Tan a = $\frac{12}{5}$

Now, ∵  Tan Ф =  $\dfrac{\textrm Perpendicular}{\textrm Base}$

So,  Tan a = $\dfrac{\textrm Perpendicular}{\textrm Base}$

Or, $\dfrac{\textrm Perpendicular}{\textrm Base}$ = $\frac{12}{5}$

Or, From Pythagoras Theorem

Hypotenuse² = perpendicular² + Base²

Or, Hypotenuse² = 12² + 5²

Or, Hypotenuse² = 144 + 25

Or, Hypotenuse² = 169

∴ Hypotenuse = $\sqrt{169}$ = $\pm$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 ×( $\dfrac{\textrm Perpendicular}{\textrm Hpotenuse}$)²

Or ,  Cos 2a = 1 - 2 ×( $\dfrac{\textrm 12}{\textrm 13}$)²

Or, Cos 2a = 1 - 2 × ($\frac{144}{169}$)

Or, Cos 2a = ($\frac{169-288}{169}$)

∴  Cos 2a = - ($\frac{119}{169}$)

Hence the value of Cos 2a is - ($\frac{119}{169}$)  . answer