What is the general solution for 3tan^2(y)=5sec(y)-1 ?

The general solution for 3tan^2(y)=5sec(y)-1 is y= pi/3+2pin,y=(5pi)/3+2pin

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3tan^2(y)=5sec(y)-1

3 tan^{2} (y) = 5 sec (y) - 1

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

Solution steps

3 tan^{2} (y) = 5 sec (y) - 1

Subtract

5 sec (y) - 1

from both sides

3 tan^{2} (y) - 5 sec (y) + 1 = 0

Rewrite using trig identities

- 2 + 3 sec^{2} (y) - 5 sec (y) = 0

Solve by substitution

sec (y) = 2, sec (y) = - \frac{1}{3}

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

sec (y) = - \frac{1}{3} :

No Solution

Combine all the solutions

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

\frac{( 1 - tan ^{2} ( a ) )}{( tan ( a ) )} = 2 cot^{2} (a)

cos (6 x) = cos (2 x)

cot (x) cos (x) - sin (x) = 1

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

tan^{2} (x) = \frac{1}{cos ( x ) + 1}

What is the general solution for 3tan^2(y)=5sec(y)-1 ?
The general solution for 3tan^2(y)=5sec(y)-1 is y= pi/3+2pin,y=(5pi)/3+2pin