Question

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Answer 1

left side

⇒

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

$\dfrac{1}{cos {}^{4}x} - \dfrac{1}{cos {}^{2} x}$

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

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

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

Apply the trig identity:

$\frac{1}{cos {}^{2} x} = (1 + tan {}^{2}x)we \: get$

$left \: side \: \\ tan {}^{2} x(1 + tan {}^{2} x) = tan {}^{4} x + tan {}^{2} x$

Answer 2

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