What is the value of cos^2(36)-sin^2(36) ?

The value of cos^2(36)-sin^2(36) is (sqrt(5)-1)/4

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cos^2(36)-sin^2(36)

cos^{2} (3 6^{\circ}) - sin^{2} (3 6^{\circ})

\frac{5 - 1}{4}

Solution steps

cos^{2} (3 6^{\circ}) - sin^{2} (3 6^{\circ})

Rewrite using trig identities:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

Rewrite using trig identities:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

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

Simplify

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

= \frac{5 - 1}{4}

csc (\frac{11 π}{12})

6 tan (3 0^{\circ})

cos (1.7)

\frac{50}{cos ( 3 0 ^{\circ} )}

cot (54 0^{\circ})

What is the value of cos^2(36)-sin^2(36) ?
The value of cos^2(36)-sin^2(36) is (sqrt(5)-1)/4