What is the value of sqrt((1+cos(75))/2) ?

The value of sqrt((1+cos(75))/2) is (sqrt(2)sqrt(4+\sqrt{6)-sqrt(2)})/4

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sqrt((1+cos(75))/2)

\frac{1 + cos ( 7 5 ^{\circ} )}{2}

\frac{2 4 + 6 - 2}{4}

Solution steps

\frac{1 + cos ( 7 5 ^{\circ} )}{2}

Rewrite using trig identities:

cos (7 5^{\circ}) = \frac{6 - 2}{4}

= \frac{1 + \frac{6 - 2}{4}}{2}

Simplify

\frac{1 + \frac{6 - 2}{4}}{2} : \frac{2 4 + 6 - 2}{4}

= \frac{2 4 + 6 - 2}{4}

4 1 + cos^{2} (\frac{7 π}{32})

450 cos (- 2 4^{\circ})

sin^{2} (\frac{\frac{π}{3}}{2})

- 8 cos (\frac{1}{2} ((4.731) + \frac{π}{3})) - 4.731

80 \cdot 20 \cdot cos (18 0^{\circ})

What is the value of sqrt((1+cos(75))/2) ?
The value of sqrt((1+cos(75))/2) is (sqrt(2)sqrt(4+\sqrt{6)-sqrt(2)})/4