Question

If root 3 sin tetha = cos tetha, find the value of 3 cos tetha + 2 cos tetha divide by 3 cos tetha + 2

Answer 1

Correct Question:-

If (√3) sin θ = cos θ , find the value of (3 cos² θ + 2 cos θ) ÷ (3 cos θ + 2).

Answer:-

Given:

(√3) sin θ = cos θ

Squaring both sides we get,

(√3)² sin² θ = cos² θ

using the identity sin² θ = 1 - cos² θ we get,

⟶ 3 (1 - cos² θ) = cos² θ

⟶ 3 - 3cos² θ - cos² θ = 0

⟶ - 4cos² θ = - 3

⟶ cos² θ = - 3/ - 4

⟶ cos² θ = 3/4

• cos θ = √3 / 2 [ By applying square root both sides ]

Now,

We have to find:

(3 cos² θ + 2 cos θ) ÷ (3 cos θ + 2)

⟶ [ 3 (3/4) + 2 (√3/2) ] ÷ [ 3(√3/2) + 2 ]

⟶ [ (9/4) + √3 ] ÷ [ (3√3/2) + 2 ]

⟶ ( 9 + 4√3 / 4 ] ÷ ( 3√3 + 4 / 2)

⟶ (9 + 4√3 / 4) * (2 / 3√3 + 4 )

⟶ √3 ( 3√3 + 4) / 2 (3√3 + 4)

⟶ √3/2

∴ The required answer is √3/2.