Question

If Sin A + Cos A equal to root 2 then show that tan A + cot a equal to 2

Answer 1

Step-by-step explanation:

here given ...

sin θ + cos θ = √2

we have to prove

tanθ + cot θ =2

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 answer

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