Question

Evaluate cos²∅ tan²∅ + tan²∅ sin²∅ in terms of tan ∅


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Answer 1

$\huge{☆Answer☆}$

$\sf\green{To \ evaluate:-}$

${\cos}^{2}θ{\tan}^{2}θ + {\tan}^{2}θ {\sin}^{2}θ$

$\sf\green{In \ term \ of:-}$

$\tanθ$

$\huge{☆Identity \ Used☆}$

$\sf\pink{☆\cosθ + \sinθ = 1☆}$

= ${\cos}^{2}θ{\tan}^{2}θ + {\tan}^{2}θ {\sin}^{2}θ$

= ${\tan}^{2}θ({\cos}^{2}θ + {\sin}^{2}θ)$

= ${\tan}^{2} θ \times 1$

= ${\tan}^{2}θ$

$\sf\huge\pink{{\cos}^{2}θ{\tan}^{2}θ + {\tan}^{2}θ{\sin}^{2}θ = {\tan}^{2}θ}$

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