What is the general solution for 2sec^2(x)-3tan(x)=2 ?

The general solution for 2sec^2(x)-3tan(x)=2 is x=0.98279…+pin,x=pin

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2sec^2(x)-3tan(x)=2

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

x = 0.98279 \dots + πn, x = πn

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{3}{2}, tan (x) = 0

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

tan (x) = 0 : x = πn

Combine all the solutions

x = arctan (\frac{3}{2}) + πn, x = πn

Show solutions in decimal form

x = 0.98279 \dots + πn, x = πn

0 = 2 (1 + cos (θ))

\frac{csc ( x )}{5} - 2 = 0

sin (4 y) + sin (6 y) + cos (y) = 0, 0 \leq y \leq \frac{π}{2}

2 \cdot cos^{2} (x) - sin^{2} (x) = 0

cos (θ) = - \frac{35}{6}

What is the general solution for 2sec^2(x)-3tan(x)=2 ?
The general solution for 2sec^2(x)-3tan(x)=2 is x=0.98279…+pin,x=pin