What is the value of cos^2((7pi)/8)-sin^2((7pi)/8) ?

The value of cos^2((7pi)/8)-sin^2((7pi)/8) is (sqrt(2))/2

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cos^2((7pi)/8)-sin^2((7pi)/8)

cos^{2} (\frac{7 π}{8}) - sin^{2} (\frac{7 π}{8})

\frac{2}{2}

Solution steps

cos^{2} (\frac{7 π}{8}) - sin^{2} (\frac{7 π}{8})

Rewrite using trig identities:

cos^{2} (\frac{7 π}{8}) = 1 - sin^{2} (\frac{7 π}{8})

= 1 - sin^{2} (\frac{7 π}{8}) - sin^{2} (\frac{7 π}{8})

Simplify

= 1 - 2 sin^{2} (\frac{7 π}{8})

Rewrite using trig identities:

sin (\frac{7 π}{8}) = sin (\frac{π}{8})

= 1 - 2 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}

sin (\frac{11 π}{20}) cos (\frac{π}{5}) + cos (\frac{11 π}{20}) sin (\frac{π}{5})

cot (arccos (- \frac{5}{6}))

arcsin (0.549)

tan (0.02)

tan (15 0^{\circ}) sin (31 5^{\circ})

What is the value of cos^2((7pi)/8)-sin^2((7pi)/8) ?
The value of cos^2((7pi)/8)-sin^2((7pi)/8) is (sqrt(2))/2