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

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

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cos^2((2pi)/5)-sin^2((2pi)/5)

cos^{2} (\frac{2 π}{5}) - sin^{2} (\frac{2 π}{5})

- \frac{5 + 1}{4}

Solution steps

cos^{2} (\frac{2 π}{5}) - sin^{2} (\frac{2 π}{5})

Rewrite using trig identities:

cos (\frac{4 π}{5})

= cos (\frac{4 π}{5})

Rewrite using trig identities:

- cos (\frac{π}{5})

= - cos (\frac{π}{5})

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

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

cos (\frac{2021 π}{4})

sec (- 15 3^{\circ})

\frac{sin ^{2} ( - π )}{sec ^{2} ( - π ) - 1}

tanh (\frac{π}{4})

ln tan (\frac{π}{3}) + sec (\frac{π}{3})

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