SSC CGL 2022 PYQ — Question 67

The correct answer is option 3 i.e. 1 +$\sqrt{3}$ 

Concept Used :

1. sin²θ + cos²θ = 1

2. sin 30⁰ = 1/2

3. sec 30⁰ = 2\$\sqrt{3}$ 

4. tan 30⁰ = 1/$\sqrt{3}$

Solution :

⇒ sin² θ - cos²θ - 3sinθ + 2 = 0              (cos²θ = 1 - sin²θ)

⇒ sin² θ - (1 - sin²θ) - 3sinθ + 2 = 0 

⇒ 2sin² θ - 3sinθ + 1 = 0

⇒ 2sin² θ - 2sinθ - sinθ + 1 = 0

⇒ 2sinθ(sinθ - 1) - 1(sinθ - 1) = 0

⇒(2sinθ -1)(sinθ -1) = 0

⇒ sinθ = 1/2 , 1

⇒ θ = 30⁰     (θ cannot be 90⁰)

Now, the required value is 1 + secθ + tanθ = 1 + sec 30⁰ + tan 30⁰

⇒ 1 +  2\$\sqrt{3}$  +  1/$\sqrt{3}$ 

⇒ (3 + $\sqrt{3}$ )/$\sqrt{3}$

⇒ 1 + $\sqrt{3}$