Question

Prove that tan ²0 + Cot^2 +2 = cosec^2 0 sec^2 0

Answer 1

We have,

LHS = tan

2

θ+cot

2

θ+2

⇒ LHS = tan

2

θ+cot

2

θ+2tanθcotθ

⇒ LHS = (tanθ+cotθ)

2

⇒ LHS = (

cosθ

sinθ

+

sinθ

cosθ

)

2

⇒ LHS = (

sinθcosθ

sin

2

θ+cos

2

θ

)

2

⇒ LHS = (

sinθcosθ

1

)

2

⇒ LHS =

sin

2

θcos

2

θ

1

=cosec

2

θsec

2

θ=RHS