What is the value of 4sqrt(1+cos^2((7pi)/(32))) ?

The value of 4sqrt(1+cos^2((7pi)/(32))) is 2sqrt(\sqrt{2-\sqrt{2+\sqrt{2)}}+6}

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4sqrt(1+cos^2((7pi)/(32)))

4 1 + cos^{2} (\frac{7 π}{32})

2 2 - 2 + 2 + 6

Solution steps

4 1 + cos^{2} (\frac{7 π}{32})

Rewrite using trig identities:

cos^{2} (\frac{7 π}{32}) = \frac{1 + cos ( \frac{7 π}{16} )}{2}

= 4 1 + \frac{1 + cos ( \frac{7 π}{16} )}{2}

4 1 + \frac{1 + cos ( \frac{7 π}{16} )}{2} = 22 cos (\frac{7 π}{16}) + 3

= 22 cos (\frac{7 π}{16}) + 3

Rewrite using trig identities:

cos (\frac{7 π}{16}) = \frac{2 - 2 + 2}{2}

= 22 \frac{2 - 2 + 2}{2} + 3

Simplify

22 \frac{2 - 2 + 2}{2} + 3 : 2 2 - 2 + 2 + 6

= 2 2 - 2 + 2 + 6

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})

\frac{sin ( \frac{π}{2} )}{( \frac{π}{2} )}

What is the value of 4sqrt(1+cos^2((7pi)/(32))) ?
The value of 4sqrt(1+cos^2((7pi)/(32))) is 2sqrt(\sqrt{2-\sqrt{2+\sqrt{2)}}+6}