Question

If 4 tan θ = 3 then (cos²θ – sin²θ) = ?

Options

• `4/25`

• `7/25`

• 1

• `11/25`

Answer 1

`bb(7/25)`

Explanation:

`tan θ = 3/4`

⇒ `(BC)/(AB) = 3/4`

 Let BC = 3k. Then, AB = 4k.

In right ΔABC, we have

AC² = AB² + BC²

= (4k)² + (3k)²

= 25k²

⇒ `AC = sqrt(25k^2)`

⇒ AC = 5k

∴ `(cos^2θ - sin^2θ) = ((AB)/(AC))^2 - ((BC)/(AC))^2`

= `((4k)/(5k))^2 - ((3k)/(5k))^2`

= `(16/25 - 9/25)`

= `7/25`