Sin theta + cos theta = root 2 then evaluate tan theta +cot theta

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Solution

sin θ + cos θ = √2
now square on both side
= ( sin θ + cos θ )² = √2²
= (sin² θ + cos² θ )+ 2 sin θ cos θ = 2
= 1+ 2sin θ cos θ = 2
=> sin θ cos θ = 1/2

now

tanθ + cot θ =sin θ/cos θ + cos θ/sin θ
=( sin² θ +cos² θ) / sin θ cos θ
= 1 / (1/2) = 2

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