Question

Prove that cos theta/1-sin theta=sec theta plike urgent

Answer 1

$\textit{\underline{\large{\underline{\red{Step by step Explanation:-}}}}}$

$\mathrm{\large{\frac{cos\Theta}{1-sin^{2}\Theta=sec\Theta}}}$

$\mathrm{\large{LHS=\frac{cos\Theta}{1-sin^{2}\Theta}}}$

$\mathrm{\large{=\frac{cos\Theta}{1-sin^{2}\Theta}\times{\frac{cos\Theta}{cos\Theta}}}}$

$\mathrm{\large{=\frac{cos^{2}\Theta}{cos\Theta(1-sin^{2}\Theta)}}}$

$\mathrm{\large{=\frac{(1-sin^{2}\Theta)}{cos\Theta(1-sin^{2}\Theta)}}}$

$\mathrm{\large{=\frac{1}{cos\Theta}}}$

$\mathrm{\large{=sec\Theta=RHS}}$

$\textit{\underline{Hence proved..}}$

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