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 tan (x) + 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

tan^{2} (x) - 2 tan (x) = 3

x, y = arcsin (x y)

9 cos^{2} (θ) - 2 sin (θ) - 9 = 6 sin (θ) - 1

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

(\frac{- 2}{2}) (sin (θ) - cos (θ)) = 0

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