What is the value of (sin(pi/8)+cos(pi/8))^2 ?

The value of (sin(pi/8)+cos(pi/8))^2 is (2+sqrt(2))/2

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(sin(pi/8)+cos(pi/8))^2

(sin (\frac{π}{8}) + cos (\frac{π}{8}))^{2}

\frac{2 + 2}{2}

Solution steps

(sin (\frac{π}{8}) + cos (\frac{π}{8}))^{2}

Rewrite using trig identities:

sin (\frac{π}{8}) + cos (\frac{π}{8}) = 2 sin (\frac{3 π}{8})

= (2 sin (\frac{3 π}{8}))^{2}

(2 sin (\frac{3 π}{8}))^{2} = 2 sin^{2} (\frac{3 π}{8})

= 2 sin^{2} (\frac{3 π}{8})

Rewrite using trig identities:

sin (\frac{3 π}{8}) = \frac{2 + 2}{2}

= 2 (\frac{2 + 2}{2})^{2}

Simplify

2 (\frac{2 + 2}{2})^{2} : \frac{2 + 2}{2}

= \frac{2 + 2}{2}

\frac{cot ^{2} ( \frac{1 ^{\circ}}{2} )}{cot ^{2} ( \frac{5 ^{\circ}}{2} )}

- 10 sin (0)

cos (- \frac{1}{2} π)

sin (2) (\frac{2 π}{3})

\frac{18}{sin ( 4.76 )}

What is the value of (sin(pi/8)+cos(pi/8))^2 ?
The value of (sin(pi/8)+cos(pi/8))^2 is (2+sqrt(2))/2