Question #788a3

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Question #788a3

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Answer 1 · 2017-05-24T19:41:19

By derivation.
Start with ${cos}^{2} (x) + {sin}^{2} (x) = 1$ $cos^2(x)+sin^2(x)=1$
Divide both sides by ${cos}^{2} (x)$ $cos^2(x)$
The result is: $1 + \frac{{sin}^{2} (x)}{{cos}^{2} (x)} = \frac{1}{{cos}^{2} (x)}$ $1 + sin^2(x)/cos^2(x) = 1/cos^2(x)$
This the same as the given equation.

Answer 2 · 2017-05-24T19:52:01

Use trig properties.

Explanation:

We know that:

$1 + {tan}^{2} θ = {sec}^{2} θ$ $1+tan^2theta=sec^2theta$

We also know that:

$sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$

Transforming the second property listed, we get:

$sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$
${(sec θ)}^{2} = {(\frac{1}{cos θ})}^{2}$ $(sectheta)^2=(1/costheta)^2$

Then applying the first property:

$1 + {tan}^{2} θ = {sec}^{2} θ = \frac{1}{{cos}^{2} θ}$ $1+tan^2theta=sec^2theta=1/cos^2theta$

$Q E D$ $QED$

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Question #788a3

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