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