Question

If Cot A + Cosec A = 3 and A is an acute angle, then what is the value of Cos A?

1. 1
2. 1/2
3. 1/3
4. 4/5

Answer 1

Correct Answer - Option 4 : 4/5

Given:

Cot A + Cosec A = 3

Calculation:

Cot A + Cosec A = 3

⇒ (Cos A /Sin A) + (1/Sin A) = 3

⇒ Cos A + 1 = 3SinA

On squaring both sides, we get

⇒ (Cos A + 1)² = 9Sin²A

⇒ Cos²A + 2CosA + 1 = 9 (1 – Cos²A)

⇒ 10Cos²A + 2Cos A – 8 = 0

⇒ 5Cos²A + Cos A – 4 = 0

⇒ (5CosA – 4) (Cos A + 1) = 0

⇒ 5CosA – 4 = 0 or Cos A + 1 = 0 

⇒ CosA = 4/5 or CosA = -1

Since, ∠A is an acute angle 

∴ cos A = 4/5