Trigonometry (C10)

If sin θ + cos θ = √2, then evaluate: tan θ + cot θ

Answer

sin θ + cos θ = √2

(sin θ + cos θ)2 = (√2)2

sin2θ + cos2θ + 2 sin θ cos θ = 2

1 + 2 sin θ cos θ = 2

sin θ cos θ = 1/2 ... (i)

We know that, sin2θ + cos2θ = 1 ... (ii)

Dividing (ii) by (i) we get

tan θ + cot θ = 2