Question

sintheta + cos theta =^2 then the value of tan theta is​

Answer 1

Answer:

Consider the given equation,

sinθ+cosθ=2      …(1)

Taking square both sides,

  sin2θ+cos2θ+2sinθcosθ=2

 1+2sinθcosθ=2

 2sinθcosθ=1

sinθcosθ=21       ……(2)

Now, divided by cosθ in equation 1st , we get

tanθ+1=cosθ2      ….(3)

Again divided by sinθ in equation 1st, we get

1+cotθ=sinθ2           ….(4)

Add equation 1st and 2nd , we get

tanθ+cotθ+2=cosθ2+sinθ2

tanθ+cotθ=2.(sinθcosθsinθ+cosθ)−2        ……(5)

Now, from equation 1st ,2nd and 5th ,we get

  tanθ+cotθ=2.⎝⎜⎜⎛