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

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

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

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

\frac{3}{2}

Solution steps

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

Rewrite using trig identities:

cos (\frac{π}{6})

= cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

= \frac{3}{2}

sin (π (1))

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

\frac{10}{sin ( 5 5 ^{\circ} )}

sin (\frac{π}{11})

sec (- 5)

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