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Trigonometrical Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometrical Identities2 Marks
Question
Prove.
$\frac{1}{1-\sin A}+\frac{1}{1+\sin A}=2 \sec ^2 A$
✓

Answer

$\text { LHS }=\frac{1}{1-\sin A}+\frac{1}{1+\sin A}$
$ =\frac{1+\sin A+1-\sin A}{(1-\sin A)(1+\sin A)}$
$ =\frac{2}{1-\sin ^2 A} $
$=\frac{2}{\cos ^2 A}$
$ =2 \sec ^2 A=\text { RHS }$

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