What is the general solution for 8sec(x)-3tan^2(x)=7 ?

The general solution for 8sec(x)-3tan^2(x)=7 is x= pi/3+2pin,x=(5pi)/3+2pin

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8sec(x)-3tan^2(x)=7

8 sec (x) - 3 tan^{2} (x) = 7

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

Solution steps

8 sec (x) - 3 tan^{2} (x) = 7

Subtract

7

from both sides

8 sec (x) - 3 tan^{2} (x) - 7 = 0

Rewrite using trig identities

- 4 - 3 sec^{2} (x) + 8 sec (x) = 0

Solve by substitution

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

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

No Solution

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

Combine all the solutions

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

sin^{2} (6 x) + sin^{2} (3 x) = 0

\frac{1}{( 2 - sin ( x ) )} = sin (x)

6 sin (x) - 3 sin^{2} (x) = 3 - cos^{2} (x)

1 - tan^{2} (x) = a^{2} + b^{2}

4 sin (x) - 4 sin^{3} (x) = 0

What is the general solution for 8sec(x)-3tan^2(x)=7 ?
The general solution for 8sec(x)-3tan^2(x)=7 is x= pi/3+2pin,x=(5pi)/3+2pin