What is the general solution for 2tan^2(x)-7sec(x)+5=0 ?

The general solution for 2tan^2(x)-7sec(x)+5=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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2tan^2(x)-7sec(x)+5=0

2 tan^{2} (x) - 7 sec (x) + 5 = 0

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Solution steps

2 tan^{2} (x) - 7 sec (x) + 5 = 0

Rewrite using trig identities

3 + 2 sec^{2} (x) - 7 sec (x) = 0

Solve by substitution

sec (x) = 3, sec (x) = \frac{1}{2}

sec (x) = 3 : x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

sec (x) = \frac{1}{2} :

No Solution

Combine all the solutions

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

cos (θ) = - \frac{3}{7}

\frac{1}{tan ( x )} + \frac{cos ^{2} ( x )}{sin ( x )} = 0

1 sin (2 5^{\circ}) = 1.506 sin (x)

\frac{1}{2} tan (2 θ) = tan (θ)

csc (x) - 3 = - 2 sin (x)

What is the general solution for 2tan^2(x)-7sec(x)+5=0 ?
The general solution for 2tan^2(x)-7sec(x)+5=0 is x=1.23095…+2pin,x=2pi-1.23095…+2pin