Sec^2 (π/4) ?

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Sec^2 (π/4) ?

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Answer 1 · 2018-03-07T13:34:19

$sec (\frac{π}{4}) = 2$ $sec(pi/4)=2$

Explanation:

$sec (x) = \frac{1}{cos (x)}$ $sec(x)=1/cos(x)$

${sec}^{2} (x) = {(\frac{1}{cos (x)})}^{2} = \frac{1}{{cos}^{2} (x)} = \frac{1}{{(cos (x))}^{2}}$ $sec^2(x)=(1/cos(x))^2 = 1/cos^2(x) = 1/(cos(x))^2$

$sec (\frac{π}{4}) = \frac{1}{{(cos (\frac{π}{4}))}^{2}}$ $sec(pi/4)=1/(cos(pi/4))^2$ $\Rightarrow$ $=>$ ${cos (\frac{π}{4}) = \frac{\sqrt{2}}{2}}$ ${cos(pi/4)=sqrt2/2}$

$sec (\frac{π}{4}) = \frac{1}{{(\frac{\sqrt{2}}{2})}^{2}}$ $sec(pi/4)=1/(sqrt2/2)^2$

$sec (\frac{π}{4}) = \frac{1}{\frac{2^{2 \cdot \frac{1}{2}}}{2^{1 \cdot 2}}}$ $sec(pi/4)=1/(2^(2*1/2)/2^(1*2)$

$sec (\frac{π}{4}) = = \frac{1}{\frac{2^{1}}{2^{2}}}$ $sec(pi/4)==1/(2^1/2^2)$

$sec (\frac{π}{4}) = \frac{1}{\frac{2}{4}}$ $sec(pi/4)=1/(2/4)$

$sec (\frac{π}{4}) = \frac{1}{\frac{1}{2}}$ $sec(pi/4)=1/(1/2)$

$sec (\frac{π}{4}) = \frac{1}{1} \div \frac{1}{2}$ $sec(pi/4)=1/1 -: 1/2$

$sec (\frac{π}{4}) = \frac{1}{1} \cdot \frac{2}{1}$ $sec(pi/4)=1/1 * 2/1$

$sec (\frac{π}{4}) = \frac{2}{1}$ $sec(pi/4)=2/1$

$sec (\frac{π}{4}) = 2$ $sec(pi/4)=2$

Thus, we have our answer.

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Sec^2 (π/4) ?

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