Prove that Tan2φ + Cot2φ + 2 = Sec2φ.Cosec2φ.

Prove that tan²Φ + cot²Φ + 2 = sec²Φ.cosec²Φ.

Sum

L.H.S. = tan²Φ + cot²Φ + 2
= tan²Φ + 1 + cot²Φ + 1
= sec²Φ + cosec²Φ

= `1/cos^2 Φ + 1/sin^2Φ`

= `(sin^2 Φ + cos^2 Φ)/(sin^2 Φ.cos^2Φ )`

= `1/(sin^2 Φ. cos^2 Φ )`

= cosec²Φ. sec²Φ
= R.H.S.
Hence proved.

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