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

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

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

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

\frac{2}{2}

Solution steps

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

Rewrite using trig identities:

cos (\frac{π}{4})

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{2}{2}

sec^{2} (- 24 π) \cdot (- 11) π

tan (arccos (\frac{12}{13}))

\frac{1}{cos ( 6 0 ^{\circ} )}

cos (7 2^{\circ}) cos (13 0^{\circ}) + sin (7 2^{\circ}) sin (13 0^{\circ})

cos (7 0^{\circ}) \cdot cos (4 0^{\circ}) + sin (7 0^{\circ}) \cdot sin (4 0^{\circ})

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