What is the general solution for 2cos^2(x)+2cos(x)-3=0 ?

The general solution for 2cos^2(x)+2cos(x)-3=0 is x=0.60434…+2pin,x=2pi-0.60434…+2pin

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2cos^2(x)+2cos(x)-3=0

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

x = 0.60434 \dots + 2 πn, x = 2 π - 0.60434 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{- 1 + 7}{2}, cos (x) = - \frac{1 + 7}{2}

cos (x) = \frac{- 1 + 7}{2} : x = arccos (\frac{- 1 + 7}{2}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 7}{2}) + 2 πn

cos (x) = - \frac{1 + 7}{2} :

No Solution

Combine all the solutions

x = arccos (\frac{- 1 + 7}{2}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 7}{2}) + 2 πn

Show solutions in decimal form

x = 0.60434 \dots + 2 πn, x = 2 π - 0.60434 \dots + 2 πn

sec^{2} (x) cot (x) = 8, 0 < x < π

tan (x) = \frac{1.5}{2}

3 csc^{2} (x) - 5 csc (x) = 2

tan (2 x) - 3 tan (x) = 0

4 sin (x) - 3 cos (x) = 0

What is the general solution for 2cos^2(x)+2cos(x)-3=0 ?
The general solution for 2cos^2(x)+2cos(x)-3=0 is x=0.60434…+2pin,x=2pi-0.60434…+2pin