Question

Prove that tan²θ + cot²θ + 2 = sec²θ + cosec²θ = sec²θ.cosec²θ

Answer 1

Step-by-step explanation:

tan²θ+cot²θ+2

=sec²θ-1+cosec²θ-1+2

=sec²θ+cosec²θ

now,sec²θ+cosec²θ

=1/cos²θ+1/sin²θ

=1/sin²θcos²θ

=sec²θcosec²θ