What is the value of sqrt((1+cos(135))/2) ?

The value of sqrt((1+cos(135))/2) is (sqrt(2-\sqrt{2)})/2

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sqrt((1+cos(135))/2)

\frac{1 + cos ( 13 5 ^{\circ} )}{2}

\frac{2 - 2}{2}

Solution steps

\frac{1 + cos ( 13 5 ^{\circ} )}{2}

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

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

Simplify

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

= \frac{2 - 2}{2}

csc (- 31 5^{\circ})

\frac{1}{2} sin (\frac{π}{2})

\frac{sin ( 4 5 ^{\circ} )}{1 - cos ( 4 5 ^{\circ} )}

arcsin (\frac{9}{17})

cos (\frac{11 π}{12}) cos (\frac{7 π}{12}) + sin (\frac{11 π}{12}) sin (\frac{7 π}{12})

What is the value of sqrt((1+cos(135))/2) ?
The value of sqrt((1+cos(135))/2) is (sqrt(2-\sqrt{2)})/2