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

1.	If sin θ + cos θ = √3 , then prove that tan θ + cot θ = 1
Answer» Solution : sin θ + cos θ = √3 (Given) or (sin θ + cos θ)² = 3 or sin² θ + cos²θ + 2sinθ cosθ = 3 2sinθ cosθ = 2 [sin²θ + cos²θ = 1] or sin θ cos θ = 1 = sin²θ + cos²θ or 1 = (sin²θ + cos²θ)/sin θ cos θ Therefore, tanθ + cotθ = 1

Answer»

Solution :

sin θ + cos θ = √3 (Given)

or (sin θ + cos θ)² = 3

or sin² θ + cos²θ + 2sinθ cosθ = 3

2sinθ cosθ = 2 [sin²θ + cos²θ = 1]

or sin θ cos θ = 1 = sin²θ + cos²θ

or 1 = (sin²θ + cos²θ)/sin θ cos θ

Therefore, tanθ + cotθ = 1

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