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

The general solution for solvefor x,tan^2(x)= 3/2 sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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solvefor x,tan^2(x)= 3/2 sec(x)

solve for

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

tan^{2} (x) = \frac{3}{2} sec (x)

Subtract

\frac{3}{2} sec (x)

from both sides

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

Simplify

tan^{2} (x) - \frac{3}{2} sec (x) : \frac{2 tan ^{2} ( x ) - 3 sec ( x )}{2}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

(- 1 + sec^{2} (x)) \cdot 2 - 3 sec (x) = 0

Solve by substitution

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

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

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

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 tan^{2} (θ) cos (θ) - tan^{2} (θ) = 0

1 + 2 cot (θ) - 2 cot^{2} (θ) = - 3 cot^{2} (θ)

3 arctan (2 x) = π

sin (x) - 9 = cos (x) - 9

7 sin (x) + 1 = 5 sin (x)

What is the general solution for solvefor x,tan^2(x)= 3/2 sec(x) ?
The general solution for solvefor x,tan^2(x)= 3/2 sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin