Question

If sin theta + cos theta = root 2
Then evaluate tan theta + cot theta

Answer 1

Answer:

Step-by-step explanation:

hello friends.....

here given ...

sin θ + cos θ = √2

we have to find

tanθ + cot θ =?

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

♦♦ hope it helps ♦♦

Answer 2

Hello friends.....

here given ...

sin θ + cos θ = √2

we have to find

tanθ + cot θ =?

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

♦♦ hope it helps ♦♦