SSC CGL 2021 PYQ — Question 58

 The correct answer is option 4 i.e. √ 5

Given :

3cos²θ - 4sinθ + 1 = 0

Formula used :

sin²θ + cos²θ = 1      ---- (1)

Calculations :

⇒ 3cos²θ - 4sinθ + 1 = 0

Using equation (1)

⇒ 3 (1 - sin²θ) - 4sinθ + 1 = 0

Put sinθ = x

⇒ 3 - 3x² - 4x + 1 = 0

⇒ 3x² + 4x - 4 = 0

⇒ 3x² + 6x - 2x - 4 = 0

⇒ 3x(x + 2) - 2(x + 2) = 0

⇒ (3x - 2) (x + 2) = 0

⇒ x = 2/3 and -2

⇒ sinθ = 2/3 and -2

We know that sinθ lies in between - 1 and 1, so

⇒ Sinθ  = 2/3

Using trigonometric ratios, we get

⇒ tanθ  = 2/$\sqrt{5}$

⇒ secθ  = 3/$\sqrt{5}$

Now, we have tanθ + secθ 

Putting the values we get

⇒   2/$\sqrt{5}$ +  3/$\sqrt{5}$

⇒ 5/$\sqrt{5}$

⇒ $\sqrt{5}$