Question

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

Answer 1

sin θ + cos θ = √3

On squaring both sides, we get

sin2θ + cos2θ + 2sin θ cos θ = 3

1 + 2sin θ cos θ = 3

sin θ cos θ = 1

Now, tan θ + cot θ

Hence Proved.