Question

sin theta +cos theta = root 2 . Find the values of tan that a +cot theta

Answer 1

given : sin θ + cos θ = √2

To find: tanθ + cot θ =?

solution:-

sin θ + cos θ = √2

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

then,

tanθ + cot θ =sin θ/cos θ + cos θ/sin θ

=( sin² θ +cos² θ) / sin θ cos θ

= 1 / (1/2)

= 2 answer