Respuesta :

Answer:

The value of Cos 2a is - ([tex]\frac{119}{169}[/tex] ) .

Step-by-step explanation:

Given as

Tan a = [tex]\frac{12}{5}[/tex]

Now, ∵  Tan Ф =  [tex]\dfrac{\textrm Perpendicular}{\textrm Base}[/tex]

So,  Tan a = [tex]\dfrac{\textrm Perpendicular}{\textrm Base}[/tex]

Or, [tex]\dfrac{\textrm Perpendicular}{\textrm Base}[/tex] = [tex]\frac{12}{5}[/tex]

Or, From Pythagoras Theorem

Hypotenuse² = perpendicular² + Base²

Or, Hypotenuse² = 12² + 5²

Or, Hypotenuse² = 144 + 25

Or, Hypotenuse² = 169

∴ Hypotenuse = [tex]\sqrt{169}[/tex] = [tex]\pm[/tex]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 ×( [tex]\dfrac{\textrm Perpendicular}{\textrm Hpotenuse}[/tex])²

Or ,  Cos 2a = 1 - 2 ×( [tex]\dfrac{\textrm 12}{\textrm 13}[/tex])²

Or, Cos 2a = 1 - 2 × ([tex]\frac{144}{169}[/tex])

Or, Cos 2a = ([tex]\frac{169-288}{169}[/tex])

∴  Cos 2a = - ([tex]\frac{119}{169}[/tex])

Hence the value of Cos 2a is - ([tex]\frac{119}{169}[/tex])  . answer

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