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  4. The value of tan 2 θ sec 2 θ( cot 2 θ- cos 2 θ) is

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Q. The value of $\tan ^{2} \theta\, \sec ^{2} \theta\left(\cot ^{2} \theta-\cos ^{2} \theta\right)$ is

Trigonometric Functions

Solution:

$\tan ^{2} \,\theta \,\sec ^{2} \theta\left(\cot ^{2} \,\theta-\cos ^{2} \theta\right)$
$=\sec ^{2} \theta\left(\tan ^{2} \theta \cot ^{2} \,\theta-\tan ^{2} \theta \cos ^{2} \,\theta\right)$
$=\sec ^{2} \,\theta\left(1-\frac{\sin ^{2} \theta}{\cos ^{2} \theta} \cos ^{2} \theta\right)=\sec ^{2} \,\theta . \cos ^{2} \,\theta=1$