What is the value of cos^2((7pi)/(12))-sin^2((7pi)/(12)) ?

The value of cos^2((7pi)/(12))-sin^2((7pi)/(12)) is 1-(2+sqrt(3))/2

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cos^2((7pi)/(12))-sin^2((7pi)/(12))

cos^{2} (\frac{7 π}{12}) - sin^{2} (\frac{7 π}{12})

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

Solution steps

cos^{2} (\frac{7 π}{12}) - sin^{2} (\frac{7 π}{12})

Rewrite using trig identities:

cos^{2} (\frac{7 π}{12}) = 1 - sin^{2} (\frac{7 π}{12})

= 1 - sin^{2} (\frac{7 π}{12}) - sin^{2} (\frac{7 π}{12})

Simplify

= 1 - 2 sin^{2} (\frac{7 π}{12})

Rewrite using trig identities:

sin (\frac{7 π}{12}) = \frac{2 ( 3 + 1 )}{4}

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

Simplify

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

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

100 \cdot sin (4 5^{\circ})

cos^{2} (2 3^{\circ})

4 (cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2}))

arctan (\frac{30}{20})

5 cos (2)

What is the value of cos^2((7pi)/(12))-sin^2((7pi)/(12)) ?
The value of cos^2((7pi)/(12))-sin^2((7pi)/(12)) is 1-(2+sqrt(3))/2