Question

Sin theta +cos theta =√3 then prove that tan theta+cos theta =1

Answer 1

Answer:

sinθ + cosθ = √3

Squaring both sides

sin²θ+cos²θ+2sinθcosθ=3

1+2sinθcosθ=3

  sinθcosθ=1

Now,

sin²θ+cos²θ=1

Divide by sinθcosθ on both sides

sinθ/cosθ + cosθ/sinθ = 1/1

tanθ + cotθ = 1

HENCE PROVED