Question

friends,,, is this solution correct or not? please it's too urgent..

Answer 1

the answer is correct but while verifying Consider RHS and in last step write LHS=RHS
.and answer is correct

Answer 2

Hi there!
Here's the answer:

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LHS =

$sec^{4}x - sec^{2}x$

= $\frac{1}{cos^{4}x} - \frac{1}{cos^{2}}$

= $\frac{1 - cos^{2}x}{cos^{4}x}$

= $\frac{sin^{2}x}{cos^{4}x}$

= $(\frac{sin^{2}x}{cos^{2}x}) (\frac{1}{cos^{2}x})$

= $tan^{2}x (\frac{1}{cos^{2}x})$

¶¶¶ We have,
$\frac{1}{cos^{2}x} = 1 + tan^{2}x$
{Trigonometrical Identity}

= $tan^{2}x (1 + tan^{2}x)$

= $tan^{4}x + tan^{2}x$

= R.H.S

Hence proved

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Hope it helps