What is the general solution for sec(x)-4=0 ?

The general solution for sec(x)-4=0 is x=1.31811…+2pin,x=2pi-1.31811…+2pin

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sec(x)-4=0

sec (x) - 4 = 0

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Solution steps

sec (x) - 4 = 0

Move

4

to the right side

sec (x) = 4

Apply trig inverse properties

x = arcsec (4) + 2 πn, x = 2 π - arcsec (4) + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

csc (θ) - cot^{2} (θ) + 1 = 0

sin (x - 4 0^{\circ}) = 1

sin (x) = - cos (x), - 2 π \leq x \leq 2 π

sin (θ) = - \frac{7}{8}

sin^{2} (x) sec (x) cot (x) = \frac{3}{2}

What is the general solution for sec(x)-4=0 ?
The general solution for sec(x)-4=0 is x=1.31811…+2pin,x=2pi-1.31811…+2pin