What is the value of 2cos^2((3pi)/5)-1 ?

The value of 2cos^2((3pi)/5)-1 is (3-sqrt(5))/4-1

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2cos^2((3pi)/5)-1

2 cos^{2} (\frac{3 π}{5}) - 1

\frac{3 - 5}{4} - 1

Solution steps

2 cos^{2} (\frac{3 π}{5}) - 1

Rewrite using trig identities:

cos (\frac{3 π}{5}) = - \frac{2 3 - 5}{4}

= 2 (- \frac{2 3 - 5}{4})^{2} - 1

Simplify

2 (- \frac{2 3 - 5}{4})^{2} - 1 : \frac{3 - 5}{4} - 1

= \frac{3 - 5}{4} - 1

\frac{4}{cos ( 5 5 ^{\circ} )}

- arctan (\frac{1 0 ^{- 1} \cdot 10}{- 1 0 ^{- 8} \cdot 1 0 ^{2} + 1})

[arcsec (\frac{5}{3}) + arcsin (\frac{5}{13})]

\frac{3}{tan ( 1 5 ^{\circ} )}

5 sin^{2} (\frac{3 π}{2})

What is the value of 2cos^2((3pi)/5)-1 ?
The value of 2cos^2((3pi)/5)-1 is (3-sqrt(5))/4-1