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Trigonometrical Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometrical Identities2 Marks
Question
Prove.$\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{\cos A}{1+\sin A}$
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Answer

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

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