How do you verify the identity $\frac{1 + sin θ}{cos θ} + \frac{cos θ}{1 + sin θ} = 2 sec θ$ $(1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta$ ?

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How do you verify the identity $\frac{1 + sin θ}{cos θ} + \frac{cos θ}{1 + sin θ} = 2 sec θ$ $(1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta$ ?

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Answer 1 · 2017-02-06T17:10:21

see below

Explanation:

Left Hand Side:

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

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

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

$=(1+2sin theta + cancel(sin^2 theta) + 1-cancel(sin^2 theta))/(cos theta(1+sin theta))$

$=(2+2sin theta)/(cos theta(1+sin theta))$

$=(2(1+sin theta))/(cos theta(1+sin theta))$

$=(2 (cancel (1+sin theta)))/(cos theta cancel((1+sin theta)))$

$=2/cos theta$

$=2*1/cos theta$

$=2sec theta$

$:.=$ Right Hand Side

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How do you verify the identity $\frac{1 + sin θ}{cos θ} + \frac{cos θ}{1 + sin θ} = 2 sec θ$ $(1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta$ ?

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Explanation:

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How do you verify the identity (1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta1+sinθcosθ+cosθ1+sinθ=2secθ(1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta?

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Explanation:

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How do you verify the identity $\frac{1 + sin θ}{cos θ} + \frac{cos θ}{1 + sin θ} = 2 sec θ$ $(1+sintheta)/costheta+costheta/(1+sintheta)=2sectheta$ ?