If tanA + cotA = 2 and A∈ (0,(π)/2 ) , then what is sinA + cosA?

If tanA + cotA = 2 and A∈ (0,(π)/2 ) , then what is sinA +…

If tanA + cotA = 2 and $A\in \left(0,\frac{\pi}{2} \right)$ , then what is sinA + cosA?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $\sqrt2$ .

tanA + cotA = 2, A ∈ (0, π/2)

⇒ tanA + 1/tanA = 2

⇒ tan²A + 1 = 2 tanA

⇒ tan²A – 2 tanA + 1 = 0

⇒ (tanA – 1)² = 0

⇒ tanA = 1

⇒ A = 45°

sin A + cos A = sin45° + cos45° = √2/2 + √2/2 = √2