How do you verify the identity $\frac{cos θ}{1 + sin θ} + tan θ = sec θ$ $costheta/(1+sintheta)+tantheta=sectheta$ ?

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How do you verify the identity $\frac{cos θ}{1 + sin θ} + tan θ = sec θ$ $costheta/(1+sintheta)+tantheta=sectheta$ ?

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Answer 1 · 2016-10-03T18:54:59

see below

Explanation:

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

Left Side $= \frac{cos θ}{1 + sin θ} + tan θ$ $=cos theta/(1+sin theta) + tan theta$

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

$= \frac{cos θ (1 - sin θ)}{1 - {sin}^{2} θ} + \frac{sin θ}{cos θ}$ $=(costheta(1-sintheta))/(1-sin^2theta)+sin theta/cos theta$

$= \frac{cos θ (1 - sin θ)}{{cos}^{2} θ} + \frac{sin θ}{cos θ}$ $=(costheta(1-sintheta))/cos^2theta +sintheta/costheta$

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

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

$= \frac{1}{cos θ}$ $=1/cos theta$

$= sec θ$ $=sec theta$

$=$ $=$ Right Side

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How do you verify the identity $\frac{cos θ}{1 + sin θ} + tan θ = sec θ$ $costheta/(1+sintheta)+tantheta=sectheta$ ?

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Explanation:

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How do you verify the identity $\frac{cos θ}{1 + sin θ} + tan θ = sec θ$ $costheta/(1+sintheta)+tantheta=sectheta$ ?