What is the general solution for 2sec(t)=tan^2(t)+1 ?

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

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2sec(t)=tan^2(t)+1

2 sec (t) = tan^{2} (t) + 1

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

Solution steps

2 sec (t) = tan^{2} (t) + 1

Subtract

tan^{2} (t) + 1

from both sides

2 sec (t) - tan^{2} (t) - 1 = 0

Rewrite using trig identities

- sec^{2} (t) + 2 sec (t) = 0

Solve by substitution

sec (t) = 0, sec (t) = 2

sec (t) = 0 :

No Solution

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

Combine all the solutions

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

2 sin (x) - 2 cos (x) = 3

8 cos (2 x) = 43

cos^{2} (θ) - sin^{2} (θ) = 1

2 cos^{2} (x) = 1 - cos (x)

cos^{3} (x) = cos^{3} (x) csc (x)

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