What is the general solution for 7cos(x)+3=3cos(x)+2 ?

The general solution for 7cos(x)+3=3cos(x)+2 is x=1.82347…+2pin,x=-1.82347…+2pin

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7cos(x)+3=3cos(x)+2

7 cos (x) + 3 = 3 cos (x) + 2

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

Solution steps

7 cos (x) + 3 = 3 cos (x) + 2

Solve by substitution

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

cos (x) = - \frac{1}{4} : x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Combine all the solutions

x = arccos (- \frac{1}{4}) + 2 πn, x = - arccos (- \frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 1.82347 \dots + 2 πn, x = - 1.82347 \dots + 2 πn

2 sin (2 θ) + 1 = 0

sin (2 x) - 2 sin (x) = 0

7 cos^{2} (x) - 1 = 5 cos (x)

x, sin (2 x) = 0

cot (θ) = - 4

What is the general solution for 7cos(x)+3=3cos(x)+2 ?
The general solution for 7cos(x)+3=3cos(x)+2 is x=1.82347…+2pin,x=-1.82347…+2pin