Prove the Following Identity : ( 1 − Tan a ) 2 + ( 1 + Tan a ) 2 = 2 Sec 2 a - Mathematics

Prove the following identity :

`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`

Sum

LHS = `(1 - tanA)^2 + (1 + tanA)^2`

= `1 + tan^2A - 2tanA + 1 + tan^2A + 2tanA`

= `2(1 + tan^2A) = 2sec^2A` = RHS

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Chapter 21: Trigonometric Identities - Exercise 21.1

Chapter 21 Trigonometric Identities
Exercise 21.1 | Q 2.02

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