What is the general solution for sec^2(x)=(sqrt(3)+1)tan(x)-sqrt(3)+1 ?

The general solution for sec^2(x)=(sqrt(3)+1)tan(x)-sqrt(3)+1 is x= pi/3+pin,x= pi/4+pin

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sec^2(x)=(sqrt(3)+1)tan(x)-sqrt(3)+1

sec^{2} (x) = (3 + 1) tan (x) - 3 + 1

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

Solution steps

sec^{2} (x) = (3 + 1) tan (x) - 3 + 1

Subtract

(3 + 1) tan (x) - 3 + 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = 3, tan (x) = 1

tan (x) = 3 : x = \frac{π}{3} + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

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

sin (z) = 100

2 cos (x) tan (x) - 1 = 0

2 sec (x) = - 2

cos (a) = \frac{3}{5}

- sin (x) + sin (2 x) = 0

What is the general solution for sec^2(x)=(sqrt(3)+1)tan(x)-sqrt(3)+1 ?
The general solution for sec^2(x)=(sqrt(3)+1)tan(x)-sqrt(3)+1 is x= pi/3+pin,x= pi/4+pin