Option 2 : 7/25

Given:

Cot θ = 4/3

Formula Used:

Cos 2θ = 2 Cos2 θ - 1 = 1 - 2 Sin2 θ

Calculation:

Here, Cot θ = Base/Perpendicular

So, B = 4 and P = 3

Now, Using the Pythagoras theorem,

H2 = P2 + B2

⇒ H = √(P2 + B2)

⇒ H = √(32 + 42)

⇒ H = √(9 + 16)

⇒ H = √(25)

⇒ H = 5

So, Cos θ = 4/5

Now,

Cos 2θ = 2 Cos2 θ - 1

⇒ 2(4/5)2 - 1

⇒ 2(16/25) - 1

⇒ (32/25) - 1

⇒ (32 - 25)/25

⇒ 7/25

∴ The value of Cos 2θ is 7/25.

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