What is the general solution for 4cos(x)=sqrt(5)-1 ?

The general solution for 4cos(x)=sqrt(5)-1 is x=1.25663…+2pin,x=2pi-1.25663…+2pin

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4cos(x)=sqrt(5)-1

4 cos (x) = 5 - 1

x = 1.25663 \dots + 2 πn, x = 2 π - 1.25663 \dots + 2 πn

Solution steps

4 cos (x) = 5 - 1

Divide both sides by

4

cos (x) = \frac{5 - 1}{4}

Apply trig inverse properties

x = arccos (\frac{5 - 1}{4}) + 2 πn, x = 2 π - arccos (\frac{5 - 1}{4}) + 2 πn

Show solutions in decimal form

x = 1.25663 \dots + 2 πn, x = 2 π - 1.25663 \dots + 2 πn

2 sin^{2} (θ) - 2 sin (θ) = 0

2 - cos (θ) = 2 + sin (θ)

sin (x) = 6757

\frac{1}{cos ( x )} + tan (x) = 2

- 5 = - 5 + 4 sin (- 2 x + \frac{3 π}{4})

What is the general solution for 4cos(x)=sqrt(5)-1 ?
The general solution for 4cos(x)=sqrt(5)-1 is x=1.25663…+2pin,x=2pi-1.25663…+2pin