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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

3

from both sides

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

Rewrite using trig identities

- 1 + sec^{4} (x) = 0

Solve by substitution

sec (x) = 1, sec (x) = - 1, sec (x) = i, sec (x) = - i

sec (x) = 1 : x = 2 πn

sec (x) = - 1 : x = π + 2 πn

sec (x) = i :

No Solution

sec (x) = - i :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

2 cos (x) - 3 = 0

cot (x) + 6 sin (x) - 2 cos (x) = 3

cos (2 θ) = cos^{2} (θ)

cos (a) = \frac{12}{13}

π cos (π x) = 0

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