What is the general solution for 3sec^2(x/2)-4sec(x/2)-4=0 ?

The general solution for 3sec^2(x/2)-4sec(x/2)-4=0 is x=(2pi)/3+4pin,x=(10pi)/3+4pin

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3sec^2(x/2)-4sec(x/2)-4=0

3 sec^{2} (\frac{x}{2}) - 4 sec (\frac{x}{2}) - 4 = 0

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Solution steps

3 sec^{2} (\frac{x}{2}) - 4 sec (\frac{x}{2}) - 4 = 0

Solve by substitution

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

sec (\frac{x}{2}) = 2 : x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

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

No Solution

Combine all the solutions

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

tan (x) = \frac{3}{10 cos ( x )}, 0^{\circ} < x < 9 0^{\circ}

2 cos^{2} (x) - 3 cos (x) = 0, 0, 2 π

2 cos^{2} (x) - 5 sin (x) = 4

2 cos (2 θ) - 7 cos (θ) + 2 = - 4 cos (θ)

sin (5 x - 15) = sin (5 \cdot x)

What is the general solution for 3sec^2(x/2)-4sec(x/2)-4=0 ?
The general solution for 3sec^2(x/2)-4sec(x/2)-4=0 is x=(2pi)/3+4pin,x=(10pi)/3+4pin