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Prove: (1 – tan A)^2 + (1 + tan A)^2 = 2sec^2 A
Prove: (1 – tan A)^2 + (1 + tan A)^2 = 2sec^2 A
Class 10 | Exercise 21A | ICSE | Selina | Trigonometrical Identities
Prove: (1 – tan A)^2 + (1 + tan A)^2 = 2sec^2 A

\[\begin{array}{*{35}{l}}

{}  \\

{{\left( 1\text{ }-\text{ }tan\text{ }A \right)}^{2}}~+\text{ }{{\left( 1\text{ }+\text{ }tan\text{ }A \right)}^{2}}  \\

=\text{ }\left( 1\text{ }+\text{ }ta{{n}^{2}}~A\text{ }+\text{ }2\text{ }tan\text{ }A \right)\text{ }+\text{ }\left( 1\text{ }+\text{ }ta{{n}^{2}}~A\text{ }-\text{ }2\text{ }tan\text{ }A \right)  \\

=\text{ }2\text{ }\left( 1\text{ }+\text{ }ta{{n}^{2}}~A \right)  \\

=\text{ }2\text{ }se{{c}^{2}}~A\text{ }\left[ Since,\text{ }1\text{ }+\text{ }ta{{n}^{2}}~A\text{ }=\text{ }se{{c}^{2}}~A \right]  \\

{}  \\

\end{array}\]

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