Question

prove that
sec²theta - cos ² theta = sin² theta ( sec²+ 1)​
plz give answer

Answer 1

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Answer 2

Answer:

${ \sec }^{2} \theta - cos {}^{2} \theta = sin {}^{2} \theta(sec {}^{2} \theta + 1) \\ \\ \\ = > sec {}^{2} \theta - (1 - {sin}^{2} \theta) \\ \\ = > \frac{1}{ {cos}^{2} \theta } - (1 - { \sin }^{2} \theta) \\ \\ = > \frac{1 - {cos}^{2} \theta + {sin}^{2} \theta. {cos}^{2} \theta }{ {cos}^{2} \theta } \\ \\ \\ = > \frac{ {sin}^{2} \theta + {sin}^{2} \theta. {cos}^{2} \theta }{ {cos}^{2} \theta} \\ \\ \\ = > \frac{ {sin}^{2} \theta(1 + {cos}^{2} \theta)}{ {cos}^{2} \theta} \\ \\ \\ = > {sin}^{2} ( \frac{1}{ {cos}^{2} \theta } + \frac{ {cos}^{2} \theta}{ {cos}^{2} \theta } ) \\ \\ \\ = > {sin}^{2} \theta( {sec}^{2} \theta + 1) \: \: proved...$

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