What is the value of 1-2sin^2((7pi)/8) ?

The value of 1-2sin^2((7pi)/8) is (sqrt(2))/2

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1-2sin^2((7pi)/8)

1 - 2 sin^{2} (\frac{7 π}{8})

\frac{2}{2}

Solution steps

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}

sec (\frac{17 π}{3})

2 sin (- \frac{π}{3}) cos (- \frac{π}{3})

csch (0)

cos (100 π)

cos (40 0^{\circ}) sec (4 0^{\circ})

What is the value of 1-2sin^2((7pi)/8) ?
The value of 1-2sin^2((7pi)/8) is (sqrt(2))/2