What is the general solution for 2sec^2(x)+tan(x)=8 ?

The general solution for 2sec^2(x)+tan(x)=8 is x=0.98279…+pin,x=-1.10714…+pin

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2sec^2(x)+tan(x)=8

2 sec^{2} (x) + tan (x) = 8

x = 0.98279 \dots + πn, x = - 1.10714 \dots + πn

Solution steps

2 sec^{2} (x) + tan (x) = 8

Subtract

8

from both sides

2 sec^{2} (x) + tan (x) - 8 = 0

Rewrite using trig identities

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

Solve by substitution

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

tan (x) = \frac{3}{2} : x = arctan (\frac{3}{2}) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.98279 \dots + πn, x = - 1.10714 \dots + πn

tan (θ) = \frac{48}{8}

- 2 cos (2 x) = 2 sin (x)

sin (θ) - 0.2 cos (θ) = \frac{7.51}{9.8}

23 = - 6 tan (θ)

- 3 - \frac{5}{2} \cdot cos (θ) = - 3 - 3 cos (θ)

What is the general solution for 2sec^2(x)+tan(x)=8 ?
The general solution for 2sec^2(x)+tan(x)=8 is x=0.98279…+pin,x=-1.10714…+pin