Q) If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1

Q29 A – Sample Question Paper – Set 1 – Maths Standard – CBSE 2026

Ans: 

Given: sin θ + cos θ = √3

Step 1: By squaring on both sides, we get:

∴ (sin θ + cos θ)² = (√3)²

∴ sin² θ + cos² θ + 2 sin θ  cos θ = 3

∵ sin² θ + cos² θ  = 1

∴ 1 + 2 sin θ  cos θ = 3

∴ 2 sin θ  cos θ = 2

∴ sin θ  cos θ = 1 ……….. (i)

Step 2: 

We need to prove that tan θ + cot θ = 1

Let’s start from LHS:

LHS = tan θ + cot θ

= (sin θ / cos θ) + (cos θ / sin θ)

= (sin² θ + cos² θ) / sin θ . cos θ

= 1 / sin θ . cos θ

By substituting value of sin θ . cos θ from equation (i), we get:

LHS = 1 / 1

= 1 = RHS

Hence Proved!

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