SSC CGL 2024 PYQ — Question 70

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

10sin²θ + 6cos²θ = 7

⇒ 10sin²θ + 6(1 - sin²θ) = 7   [∵ cos²θ = 1 - sin²θ]

⇒ 10sin²θ + 6 - 6sin²θ = 7

⇒ 4sin²θ = 1

⇒ sin²θ = 1/4

⇒ sinθ = 1/2 = sin 30°

⇒ θ = 30°

⇒ tanθ = tan 30° = 1/√3

Therefore, the value of tanθ is 1/√3.