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Trigonometric Identities

Prove that ...

Question

Prove that $(1 - t a n A)^{2} + (1 + t a n A)^{2} = 2 s e c^{2} A$

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Solution

Taking L.H.S,
$(1 - t a n A)^{2} + (1 + t a n A)^{2}$
$= (1 + t a n^{2} A + 2 t a n A) + (1 + t a n^{2} - 2 t a n A)$
$= 2 (1 + t a n^{2} A)$
$= 2 s e c^{2} A$ [Since, $1 + t a n^{2} A = s e c^{2} A$ ]
-Hence Proved

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{(1 - t a n A)}^{2} + {(1 + t a n A)}^{2} = 2 s e c^{2} A

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