Which of the following is true when x = Sin A + Cos A; y = Sec A + Cosec A?

Question

Question

This question was previously asked in

SSC CPO 2024 Official Paper-I (Held On: 27 Jun, 2024 Shift 3)

Answer 1

Given:

x = Sin A + Cos A

y = Sec A + Cosec A

Formula used:

We know:

Calculations:

Square x:

⇒ x² = (Sin A + Cos A)²

⇒ x² = Sin² A + Cos² A + 2Sin A × Cos A

⇒ x² = 1 + 2Sin A × Cos A

⇒ (x2 - 1)/2 = Sin A × Cos A ...........(i)

Square y:

⇒ y = 1/Cos A + 1/Sin A

⇒ y = (Sin A + Cos A)/SinACosA

Put value from above details,

⇒ y = x/[(x2 - 1)/2]

⇒ y = 2x/(x2 - 1)

⇒ y(x2 - 1) = 2x

⇒ yx2 - y = 2x

⇒ x2y = 2x + y

∴ Option 1 is the correct answer.

Download Solution PDF