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

The general solution for 2sec^2(x)-5tan(x)=5 is x=1.24904…+pin,x=-0.46364…+pin

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2sec^2(x)-5tan(x)=5

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

x = 1.24904 \dots + πn, x = - 0.46364 \dots + πn

Solution steps

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

Subtract

5

from both sides

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

Rewrite using trig identities

- 3 + 2 tan^{2} (x) - 5 tan (x) = 0

Solve by substitution

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

tan (x) = 3 : x = arctan (3) + πn

tan (x) = - \frac{1}{2} : x = arctan (- \frac{1}{2}) + πn

Combine all the solutions

x = arctan (3) + πn, x = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

x = 1.24904 \dots + πn, x = - 0.46364 \dots + πn

coth (z) = 1

cos (10 x) = sin (5 x - 3)

13 tan (a) = 10, 0 b = 100

- 4 cos (3 x) = 0

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( 65.3 8 ^{\circ} )}{sin ( x )}

What is the general solution for 2sec^2(x)-5tan(x)=5 ?
The general solution for 2sec^2(x)-5tan(x)=5 is x=1.24904…+pin,x=-0.46364…+pin