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Question Number 106609 by DeepakMahato last updated on 06/Aug/20
Prove that  (1−sin^2 θ)sec^2 θ=1
$${Prove}\:{that} \\ $$$$\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right){sec}^{\mathrm{2}} \theta=\mathrm{1} \\ $$
Commented by mohammad17 last updated on 06/Aug/20
when:1−sin^2 θ=cos^2 θ  when:sec^2 θ=(1/(cos^2 θ))    ⌋(1−sin^2 θ)sec^2 θ=cos^2 θ×(1/(cos^2 θ))=1       m.ss.mohammad
$${when}:\mathrm{1}−{sin}^{\mathrm{2}} \theta={cos}^{\mathrm{2}} \theta \\ $$$${when}:{sec}^{\mathrm{2}} \theta=\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \theta} \\ $$$$ \\ $$$$\rfloor\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right){sec}^{\mathrm{2}} \theta={cos}^{\mathrm{2}} \theta×\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \theta}=\mathrm{1} \\ $$$$ \\ $$$$\:\:\:{m}.{ss}.{mohammad} \\ $$
Answered by JDamian last updated on 06/Aug/20
(1−(1−cos^2 θ))(1/(cos^2 θ))=cos^2 θ (1/(cos^2 θ)) = 1
$$\left(\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \theta\right)\right)\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \theta}=\mathrm{cos}^{\mathrm{2}} \theta\:\frac{\mathrm{1}}{\mathrm{cos}^{\mathrm{2}} \theta}\:=\:\mathrm{1} \\ $$

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