Question

Prove the identity


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Answer 1

$\mathfrak{\huge{Answer:-}}\\ (1 - {cos}^{2}θ ) {sec}^{2} θ = {tan}^{2} θ\\ {sin}^{2} θ \times {sec}^{2}θ = {tan}^{2}θ \: \: (1 - {cos}^{2}θ = {sin}^{2}θ ) \\ {sin}^{2}θ \times \frac{1}{ {cos}^{2}θ } = {tan}^{2} θ( {sec}^{2}θ = \frac{1}{ {cos}^{2} θ} ) \\ \frac{ {sin}^{2} θ}{ {cos}^{2}θ } = {tan}^{2} θ\\ {tan}^{2}θ = {tan}^{2}θ \\LHS=RHS\\Hence \: proved$