What is the general solution for cos^2(5x)=1 ?

The general solution for cos^2(5x)=1 is x=(2pin)/5 ,x= pi/5+(2pin)/5

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cos^2(5x)=1

cos^{2} (5 x) = 1

x = \frac{2 πn}{5}, x = \frac{π}{5} + \frac{2 πn}{5}

Solution steps

cos^{2} (5 x) = 1

Solve by substitution

cos (5 x) = 1, cos (5 x) = - 1

cos (5 x) = 1 : x = \frac{2 πn}{5}

cos (5 x) = - 1 : x = \frac{π}{5} + \frac{2 πn}{5}

Combine all the solutions

x = \frac{2 πn}{5}, x = \frac{π}{5} + \frac{2 πn}{5}

1 = 1 - 2 arctan (\frac{1 - 2 - C}{1 - C})

x, 1 + 2 sin (x) = 0

sin (x) = \frac{- 5}{13}

sin^{2} (θ) - cos^{2} (θ) + cos (θ) = 0

3 sin^{2} (x) = 9 cos^{2} (x)

What is the general solution for cos^2(5x)=1 ?
The general solution for cos^2(5x)=1 is x=(2pin)/5 ,x= pi/5+(2pin)/5