What is the general solution for 4cos(4x)=3 ?

The general solution for 4cos(4x)=3 is x=(0.72273…)/4+(pin)/2 ,x= pi/2-(0.72273…)/4+(pin)/2

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4cos(4x)=3

4 cos (4 x) = 3

x = \frac{0.72273 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.72273 \dots}{4} + \frac{πn}{2}

Solution steps

4 cos (4 x) = 3

Divide both sides by

4

cos (4 x) = \frac{3}{4}

Apply trig inverse properties

4 x = arccos (\frac{3}{4}) + 2 πn, 4 x = 2 π - arccos (\frac{3}{4}) + 2 πn

Solve

4 x = arccos (\frac{3}{4}) + 2 πn : x = \frac{arccos ( \frac{3}{4} )}{4} + \frac{πn}{2}

Solve

4 x = 2 π - arccos (\frac{3}{4}) + 2 πn : x = \frac{π}{2} - \frac{arccos ( \frac{3}{4} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{3}{4} )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( \frac{3}{4} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.72273 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.72273 \dots}{4} + \frac{πn}{2}

tan (y) = - 2

sin (θ) = - \frac{2}{2}

sin^{2} (x) + sin (x) \cdot cos (x) + cos^{2} (x) = 10

x, sin (x) = \frac{2}{3}

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

What is the general solution for 4cos(4x)=3 ?
The general solution for 4cos(4x)=3 is x=(0.72273…)/4+(pin)/2 ,x= pi/2-(0.72273…)/4+(pin)/2