Question

if sin theta + cos theta=root2 then evalute tan theta +cot theta

Answer 1

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

=nswer:

ACOORDING TO THE QUESTION,

we have to find tanФ+cosФ ,

now,we can  square it both sides,so,( sinФ+cosФ)²=(√2)²

as, (a+b)²=a²+b²+2ab

now, it becomes (sin²Ф+cos²Ф)+2 sinФ cosФ=2

1+2sinФcosФ=2

sinФcosФ=1/2

now , we have to evaluate tanФ+cosФ

so, tanФ+cotФ as,tanФ=sin/cos and cosФ=cos/sin

= sin/cos + cos/sin

now, sin²Ф+cos²Ф/ sinФcosФ=1/1/2=2

hence,2 is the answer.

i hope it helps uh

Step-by-step explanation: