If sin theta +cos theta= root 2

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

Thank you

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