What is the value of (2cos(pi/4)-sin((3pi)/4))/(1-cos(pi/4)) ?

The value of (2cos(pi/4)-sin((3pi)/4))/(1-cos(pi/4)) is sqrt(2)+1

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(2cos(pi/4)-sin((3pi)/4))/(1-cos(pi/4))

\frac{2 cos ( \frac{π}{4} ) - sin ( \frac{3 π}{4} )}{1 - cos ( \frac{π}{4} )}

2 + 1

Solution steps

\frac{2 cos ( \frac{π}{4} ) - sin ( \frac{3 π}{4} )}{1 - cos ( \frac{π}{4} )}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= \frac{2 \cdot \frac{2}{2} - \frac{2}{2}}{1 - \frac{2}{2}}

Simplify

\frac{2 \cdot \frac{2}{2} - \frac{2}{2}}{1 - \frac{2}{2}} : 2 + 1

= 2 + 1

arcsin (\frac{3}{6})

cos (\frac{6}{8})

6 + 3 cos (\frac{π}{4})

20 \cdot sin (5 0^{\circ})

tan (- 8)

What is the value of (2cos(pi/4)-sin((3pi)/4))/(1-cos(pi/4)) ?
The value of (2cos(pi/4)-sin((3pi)/4))/(1-cos(pi/4)) is sqrt(2)+1