1.

Show that tan2 θ + cot2 θ ≥ 2 for all θ ∈ R

Answer»

tanθ + cot2 θ = tanθ + 1/tanθ 

(tan θ)2 + (1/tan θ)2

= (tan θ - 1/ tan θ)2 + 2tan θ1/ tan θ

                ...[∴a2 + b2 = (a-b)2 + 2ab]

= (tan θ - 1/ tan θ)+ 2 ≥ 2 for all θ ∈R.



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