What is the value of cos^2(pi/(12))-cos^2((5pi)/(12)) ?

The value of cos^2(pi/(12))-cos^2((5pi)/(12)) is (sqrt(3))/2

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cos^2(pi/(12))-cos^2((5pi)/(12))

cos^{2} (\frac{π}{12}) - cos^{2} (\frac{5 π}{12})

\frac{3}{2}

Solution steps

cos^{2} (\frac{π}{12}) - cos^{2} (\frac{5 π}{12})

Rewrite using trig identities:

cos (\frac{π}{12}) = \frac{6 + 2}{4}

Rewrite using trig identities:

cos (\frac{5 π}{12}) = \frac{6 - 2}{4}

= (\frac{6 + 2}{4})^{2} - (\frac{6 - 2}{4})^{2}

Simplify

(\frac{6 + 2}{4})^{2} - (\frac{6 - 2}{4})^{2} : \frac{3}{2}

= \frac{3}{2}

sin (2 0^{\circ}) cos (2 5^{\circ}) + cos (2 0^{\circ}) sin (2 5^{\circ})

\frac{5}{cos ( 3 0 ^{\circ} )}

arcsin (0.51)

tan (8 3^{\circ})

cos (1.4)

What is the value of cos^2(pi/(12))-cos^2((5pi)/(12)) ?
The value of cos^2(pi/(12))-cos^2((5pi)/(12)) is (sqrt(3))/2