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  4. The value of tan2 θ sec2 θ (cot2θ - cos2θ) 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:

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