SSC CGL 2022 PYQ — Question 69

The correct answer is option 1 i.e. 5/4.

Given, 3sec² θ + tanθ - 7 =0

Put θ = 45°

⇒  3sec² 45°+ tan45° - 7 = 3 × 2 + 1 - 7 = 7 - 7 = 0

Thus, θ = 45° satisfies our given equation.

Put θ = 45° in $(2sinθ + 3cosθ)\over (cosec θ + secθ)$

⇒ $(2sinθ + 3cosθ)\over (cosec θ + secθ)$ = (2sin45° + 3cos45°)/(cosec45° + sec45°)

⇒ {2 × (1/2)^1/2 + 3 × (1/2)^1/2}/{(2)^1/2 + (2)^1/2}

⇒ {5/(2)^1/2}/{2 × (2)^1/2} = 5/{2 × (2)^1/2 × (2)^1/2} 

⇒ 5/4