What is the value of cos^2(165)-sin^2(165) ?

The value of cos^2(165)-sin^2(165) is 1-(2-sqrt(3))/2

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cos^2(165)-sin^2(165)

cos^{2} (16 5^{\circ}) - sin^{2} (16 5^{\circ})

1 - \frac{2 - 3}{2}

Solution steps

cos^{2} (16 5^{\circ}) - sin^{2} (16 5^{\circ})

Rewrite using trig identities:

cos^{2} (16 5^{\circ}) = 1 - sin^{2} (16 5^{\circ})

= 1 - sin^{2} (16 5^{\circ}) - sin^{2} (16 5^{\circ})

Simplify

= 1 - 2 sin^{2} (16 5^{\circ})

Rewrite using trig identities:

sin (16 5^{\circ}) = \frac{6 - 2}{4}

= 1 - 2 (\frac{6 - 2}{4})^{2}

Simplify

1 - 2 (\frac{6 - 2}{4})^{2} : 1 - \frac{2 - 3}{2}

= 1 - \frac{2 - 3}{2}

15 \cdot sin (6 0^{\circ})

sec (arccos (- \frac{2}{2}))

sin (π \cdot 1)

sin (0.05)

cos^{2} (\frac{π}{12}) - cos^{2} (\frac{5 π}{12})

What is the value of cos^2(165)-sin^2(165) ?
The value of cos^2(165)-sin^2(165) is 1-(2-sqrt(3))/2