Question

2. If sin°ø+cos°ø = √3, then prove tan° ø + cot°ø=1​

Answer 1

Step-by-step explanation:

sinθ+cosθ=

3

=(sinθ+cosθ)

2

=3

=sin

2

θ+cos

2

θ+2sinθcosθ=3

⇒2sinθcosθ=2

⇒sinθcosθ=1

⇒sinθcosθ=sin

2

θ+cos

2

θ

⇒1=

sinθcosθ

sin

2

θ+cos

2

θ

⇒tanθ+cotθ=1

Answer 2

Answer:

sinθ+cosθ= ✓3

=(sinθ+cosθ) ^2=3

sin^2θ+cos^2θ+2sinθcosθ=3

=> 2sinθcosθ=2

=> sinθcosθ=1

=> sinθcosθ=sin^2θ+cos^2θ

1= sin^2θ+cos^2θ/sinθcosθ

=> tanθ+cotθ=1