What is the value of 2cos^2((5pi)/8)-1 ?

The value of 2cos^2((5pi)/8)-1 is -(sqrt(2))/2

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2cos^2((5pi)/8)-1

2 cos^{2} (\frac{5 π}{8}) - 1

- \frac{2}{2}

Solution steps

2 cos^{2} (\frac{5 π}{8}) - 1

Rewrite using trig identities:

cos (\frac{5 π}{8}) = - cos (\frac{3 π}{8})

= 2 (- cos (\frac{3 π}{8}))^{2} - 1

2 (- cos (\frac{3 π}{8}))^{2} - 1 = 2 cos^{2} (\frac{3 π}{8}) - 1

= 2 cos^{2} (\frac{3 π}{8}) - 1

Rewrite using trig identities:

cos (\frac{3 π}{4})

= cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= - \frac{2}{2}

2 sin (4)

arctan (\frac{16}{12})

8 cos (8)

sin (93 0^{\circ})

5 arctan (1) - 1

What is the value of 2cos^2((5pi)/8)-1 ?
The value of 2cos^2((5pi)/8)-1 is -(sqrt(2))/2