Question

If sin theta + cos theta = root2 then evaluate tan theta + cot theta

Answer 1

sin+cos=√2
tan +cot
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

Answer 2

sin theta + cos theta = root 2

=> sin square theta + cos square theta + 2 sin theta cos theta = 2

=> 1+ 2 sin theta cos theta = 2
sin theta cos theta = 1/2

now ,

tan theta + cot theta
= sin theta/ (cos theta) + cos theta/ (sin theta)
= (sin square theta + cos square theta)/( sin theta cos theta)
= 1/(1/2)
= 2