1√(1+4x^2) ⇒ 1√(1^2+(2x)^2)√(1^2 (2x)^2)√(1 (2x)^2) ⇒ √(1 (2x)^2)√(1^2 (2x)^4) ⇒ [√(1 4x^2)√(1 16x^4). ...

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Evaluate 1√1...

Question

Evaluate
$\frac{1}{\sqrt{1 + 4 x^{2}}}$

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Solution

$\frac{1}{\sqrt{1 + 4 x^{2}}}$
$\Rightarrow \frac{1}{\sqrt{1^{2} + (2 x)^{2}}} \frac{\sqrt{1^{2} - (2 x)^{2}}}{\sqrt{1 - (2 x)^{2}}}$
$\Rightarrow \frac{\sqrt{1 - (2 x)^{2}}}{\sqrt{1^{2} - (2 x)^{4}}}$
$\Rightarrow [\frac{\sqrt{1 - 4 x^{2}}}{\sqrt{1 - 16 x^{4}}}$

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