What is the general solution for cos^5(x)=sin(75) ?

The general solution for cos^5(x)=sin(75) is x=0.11762…+360n,x=360-0.11762…+360n

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cos^5(x)=sin(75)

cos^{5} (x) = sin (7 5^{\circ})

x = 0.11762 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 0.11762 \dots + 36 0^{\circ} n

Solution steps

cos^{5} (x) = sin (7 5^{\circ})

sin (7 5^{\circ}) = \frac{6 + 2}{4}

cos^{5} (x) = \frac{6 + 2}{4}

For

x^{n} = f (a)

, n is odd, the solution is

Apply trig inverse properties

Show solutions in decimal form

x = 0.11762 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 0.11762 \dots + 36 0^{\circ} n

csc^{2} (x) = sec (x)

(2 cos (x) - sin^{2} (x)) = 1 + cos^{2} (x)

6 cos^{3} (x) + cos^{2} (x) - 1 = 0

4 tan^{2} (x) + 12 tan (x) - 27 = 0

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

What is the general solution for cos^5(x)=sin(75) ?
The general solution for cos^5(x)=sin(75) is x=0.11762…+360n,x=360-0.11762…+360n