⇒ (1+tan A)^2+(1 tan A)^2 = (1 + tan^2 A + 2tan A) + (1 + tan^2 A 2tan A) =(2 nbsp;+ 2tan^2 A nbsp;+ 2tan A 2tan A) nbsp; =(2 nbsp;+ 2tan^2 A) =2(1+ ...

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Standard X

Mathematics

Trigonometric Identities

1+tan A2 + 1-...

Question

$(1 + tan A)^{2} + (1 - tan A)^{2} =$

$2$

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$1$

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$2 {sec}^{2} A$

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$2 {cos}^{2} A$

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Solution

The correct option is C
$2 {sec}^{2} A$

$\Rightarrow (1 + tan A)^{2} + (1 - tan A)^{2}$
$= (1 + {tan}^{2} A + 2 tan A) + (1 + {tan}^{2} A - 2 tan A)$
$= (2 + 2 {tan}^{2} A + 2 tan A - 2 tan A)$
$= (2 + 2 {tan}^{2} A)$
$= 2 (1 + {tan}^{2} A)$
$= 2 {sec}^{2} A$

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(1+tan A)2+(1−tan A)2=

The correct option is C 2 sec2 A ⇒(1+tanA)2+(1−tanA)2 =(1+tan2A+2tanA)+(1+tan2A−2tanA) =(2+2tan2A+2tanA−2tanA) =(2+2tan2A) =2(1+tan2A) =2sec2A

$(1 + tan A)^{2} + (1 - tan A)^{2} =$

The correct option is C
$2 {sec}^{2} A$

$\Rightarrow (1 + tan A)^{2} + (1 - tan A)^{2}$
$= (1 + {tan}^{2} A + 2 tan A) + (1 + {tan}^{2} A - 2 tan A)$
$= (2 + 2 {tan}^{2} A + 2 tan A - 2 tan A)$
$= (2 + 2 {tan}^{2} A)$
$= 2 (1 + {tan}^{2} A)$
$= 2 {sec}^{2} A$