What is the value of (sin(15)+sin(75))^6 ?

The value of (sin(15)+sin(75))^6 is 27/8

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(sin(15)+sin(75))^6

(sin (1 5^{\circ}) + sin (7 5^{\circ}))^{6}

\frac{27}{8}

Solution steps

(sin (1 5^{\circ}) + sin (7 5^{\circ}))^{6}

Rewrite using trig identities:

sin (1 5^{\circ}) + sin (7 5^{\circ}) = 2 sin (4 5^{\circ}) cos (3 0^{\circ})

= (2 sin (4 5^{\circ}) cos (3 0^{\circ}))^{6}

Simplify

= 64 sin^{6} (4 5^{\circ}) cos^{6} (3 0^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

= 64 (\frac{2}{2})^{6} (\frac{3}{2})^{6}

Simplify

64 (\frac{2}{2})^{6} (\frac{3}{2})^{6} : \frac{27}{8}

= \frac{27}{8}

sin (\frac{17 π}{12}) + sin (\frac{13 π}{12})

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

cos (- \frac{7 π}{2})

csc (\frac{- π}{6})

arcsin (0.26)

What is the value of (sin(15)+sin(75))^6 ?
The value of (sin(15)+sin(75))^6 is 27/8