Question

Sin +cos = root 2
Then find
tan +cot=?

Answer 1

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

Answer 2

Hey !!!

sin + cos = √2

if we squaring on both side we get

(sin + cos )² = (√2)²

=sin² + cos² + 2sin * cos = 2

= 1 + 2sin* cos = 2

= 2sin * cos = 2 -1

= sin * cos = 1/2 ------------1)

now ,

tan + cot = ?

= sin/cos + cos/sin

sin² + cos² /sin* cos

•°• sin² + cos² = 1

so, 1/sin* cos

=1/1/2 [ from equation 1 ]

= 2 Answer

Hope it helps you !!!

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