Question

If sinø+cosø=root3 then prove that tan ø+cosø=1​

Answer 1

Answer:

Answer

sinθ+cosθ=3

=(sinθ+cosθ)2=3

=sin2θ+cos2θ+2sinθcosθ=3

⇒2sinθcosθ=2

⇒sinθcosθ=1

⇒sinθcosθ=sin2θ+cos2θ

⇒1=sinθcosθsin2θ+cos2θ

⇒tanθ+cotθ=1

Answer 2

Answer:

sinθ+cosθ= √3

Squaring both sides

=(sinθ+cosθ)²=3

=sin²θ+cos²θ+2sinθcosθ=3

⇒1+2sinθcosθ=3 (°.°sin²θ+cos²θ=1)

⇒sinθcosθ=1

⇒sinθcosθ=sin²θ+cos²θ

(°.°sin²θ+cos²θ=1)

⇒1=sin²θ+cos²θ/sinθcosθ

⇒tanθ+cotθ=1