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Prove that= Cos theta/ 1+sin theta=1-sin theta/ cos theta ?

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May 24, 2018

$\frac{cos (θ)}{1 + sin (θ)} = \frac{1 - sin (θ)}{cos (θ)}$ $cos(theta)/(1+sin(theta))=(1-sin(theta))/cos(theta)$

$L S = \frac{cos (θ)}{1 + sin (θ)} \cdot \frac{1 - sin (θ)}{1 - sin (θ)}$ $LS=cos(theta)/(1+sin(theta))*(1-sin(theta))/(1-sin(theta))$

$= \frac{cos (θ) (1 - sin (θ))}{1 - {sin}^{2} (θ)}$ $=[cos(theta)(1-sin(theta))]/(1-sin^2(theta))$

$= \frac{cos (θ) (1 - sin (θ))}{{cos}^{2} (θ)}$ $=[cos(theta)(1-sin(theta))]/(cos^2(theta))$

$= \frac{1 - sin (θ)}{cos (θ)} = R S$ $=(1-sin(theta))/cos(theta)=RS$

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