What is the general solution for cos^2(36)-sin^2(36)=cos(x) ?

The general solution for cos^2(36)-sin^2(36)=cos(x) is x=1.25663…+360n,x=360-1.25663…+360n

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

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

x = 1.25663 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 1.25663 \dots + 36 0^{\circ} n

Solution steps

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

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

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

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

Switch sides

cos (x) = (\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}

Apply trig inverse properties

x = arccos (\frac{5 - 1}{4}) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (\frac{5 - 1}{4}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.25663 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 1.25663 \dots + 36 0^{\circ} n

23 cos (x) = - 17 - cos (x)

8 cos^{2} (θ) + 14 cos (θ) - 11 = 8 cos (θ) - 6

tan (x) cos (x) + cos (x) = 0

sin^{2} (x) (tan^{2} (x)) = 1 - sin^{2} (x)

2 sin^{2} (x) = 3 - 5 cos (x)

What is the general solution for cos^2(36)-sin^2(36)=cos(x) ?
The general solution for cos^2(36)-sin^2(36)=cos(x) is x=1.25663…+360n,x=360-1.25663…+360n