Answer:
You have to apply Trigonometry Formula :
[tex] {sin}^{2} θ + {cos}^{2} θ = 1[/tex]
[tex]1 + {tan}^{2} θ = {sec}^{2} θ[/tex]
Next, you have to prove it :
[tex](1 + {tan}^{2} θ)(1 - {cos}^{2} θ) = {tan}^{2} θ[/tex]
[tex]LHS = (1 + {tan}^{2} θ)(1 - {cos}^{2} θ)[/tex]
[tex]LHS = ( {sec}^{2} θ)( {sin}^{2} θ)[/tex]
[tex]LHS = ( \frac{1}{ {cos}^{2} θ} )( {sin}^{2} θ)[/tex]
[tex]LHS = \frac{ {sin}^{2} θ}{ {cos}^{2} θ} [/tex]
[tex]LHS = {tan}^{2} θ[/tex]
[tex]∴LHS = RHS \: (proven)[/tex]
