Question

2sinθ + cosθ=sqrt 5 then tanθ +cotθ=?

Answer 1

Answer:

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.