If 0 ≤ θ ≤ 90°, and cosθ + secθ = 2, Then θ is equal to:

SSC Selection Post 2019 PYQ — Question 68

If 0 $\leq$ θ $\leq$ 90°, and cosθ + secθ = 2, Then θ is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 0°.

cosθ + secθ = 2

⇒ cosθ + 1/cosθ = 2

⇒ cos²θ + 1 = 2cosθ

⇒ cos²θ - 2cosθ + 1 = 0

⇒ (cosθ - 1)² = 0

⇒ cosθ = 1

⇒ θ = 0°