How do you express $cos θ - {cos}^{2} θ + sec θ$ $cos theta - cos^2 theta + sec theta$ in terms of $sin θ$ $sin theta$ ?

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How do you express $cos θ - {cos}^{2} θ + sec θ$ $cos theta - cos^2 theta + sec theta$ in terms of $sin θ$ $sin theta$ ?

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Answer 1 · 2016-03-10T04:09:18

$\sqrt{1 - {sin}^{2} θ} - (1 - {sin}^{2} θ) + \frac{1}{\sqrt{1 - {sin}^{2} θ}}$ $sqrt(1-sin^2 theta)-(1-sin^2 theta)+1/sqrt(1-sin^2 theta)$
just simplify it further if you need to.

Explanation:

From the given data:
How do you express $cos θ - {cos}^{2} θ + sec θ$ $cos theta−cos^2 theta+sec theta$ in terms of
$sin θ$ $sin theta$ ?

Solution:

from the fundamental trigonometric identities

${sin}^{2} θ + {cos}^{2} θ = 1$ $Sin^2 theta+Cos^2 theta=1$
it follows

$cos θ = \sqrt{1 - {sin}^{2} θ}$ $cos theta=sqrt(1-sin^2 theta)$

${cos}^{2} θ = 1 - {sin}^{2} θ$ $cos^2 theta=1-sin^2 theta$

also

$sec θ = \frac{1}{cos θ}$ $sec theta=1/cos theta$

therefore

$cos θ - {cos}^{2} θ + sec θ$ $cos theta−cos^2 theta+sec theta$

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

God bless...I hope the explanation is useful.

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How do you express $cos θ - {cos}^{2} θ + sec θ$ $cos theta - cos^2 theta + sec theta$ in terms of $sin θ$ $sin theta$ ?

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Explanation:

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