What is the general solution for 2tan(x)+sec^2(x)=4 ?

The general solution for 2tan(x)+sec^2(x)=4 is x= pi/4+pin,x=-1.24904…+pin

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2tan(x)+sec^2(x)=4

2 tan (x) + sec^{2} (x) = 4

x = \frac{π}{4} + πn, x = - 1.24904 \dots + πn

Solution steps

2 tan (x) + sec^{2} (x) = 4

Subtract

4

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 3 : x = arctan (- 3) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (- 3) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = - 1.24904 \dots + πn

cos (a) + sin (a) = 1

cos (x) = \frac{1}{7}

sin (5 x + 43) = cos (- x + 3 1^{\circ})

sin (x) + 1 = 2 cos^{2} (x)

x, arctan (x^{2} + 9 y^{2} - 2 x - 36 y + 37) = 0

What is the general solution for 2tan(x)+sec^2(x)=4 ?
The general solution for 2tan(x)+sec^2(x)=4 is x= pi/4+pin,x=-1.24904…+pin