Prove that : cosec2 45° - cot2 45° = 1

cosec2 45° - cot2 45° = 1 L.H.S. = cosec2 45° - cot2 45° R.H.S. = 1 ∴ L.H.S. = R.H.S. Hence proved, cosec2 45° - cot2 45° = 1.

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Mathematics

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cosec² 45° - cot² 45° = 1

L.H.S. = cosec² 45° - cot² 45°

$= (\sqrt2)^2 - (1)^2 \\[1em] = 2 - 1\\[1em] = 1$

R.H.S. = 1

∴ L.H.S. = R.H.S.

Hence proved, cosec² 45° - cot² 45° = 1.

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