What is the value of (2-sqrt(2)sin(pi/4))/(cos(pi/4)) ?

The value of (2-sqrt(2)sin(pi/4))/(cos(pi/4)) is square root of 2

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(2-sqrt(2)sin(pi/4))/(cos(pi/4))

\frac{2 - 2 sin ( \frac{π}{4} )}{cos ( \frac{π}{4} )}

2

Solution steps

\frac{2 - 2 sin ( \frac{π}{4} )}{cos ( \frac{π}{4} )}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{2 - 2 \frac{2}{2}}{\frac{2}{2}}

Simplify

\frac{2 - 2 \frac{2}{2}}{\frac{2}{2}} : 2

= 2

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What is the value of (2-sqrt(2)sin(pi/4))/(cos(pi/4)) ?
The value of (2-sqrt(2)sin(pi/4))/(cos(pi/4)) is square root of 2