Question
Prove.
$(1-\tan A)^2+(1+\tan A)^2=2 \sec ^2 A$
$(1-\tan A)^2+(1+\tan A)^2=2 \sec ^2 A$
✓
Answer
$\text { LHS }=(1-\tan A)^2+(1+\tan A)^2$
$=\left(1+\tan ^2 A-2 \tan A\right)+\left(1+\tan ^2 A+2 \tan A\right)$
$=2\left(1+\tan ^2 A\right) $
$=2 \sec ^2 A=\text { RHS }$
$=\left(1+\tan ^2 A-2 \tan A\right)+\left(1+\tan ^2 A+2 \tan A\right)$
$=2\left(1+\tan ^2 A\right) $
$=2 \sec ^2 A=\text { RHS }$
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