What is the general solution for sec^2(x)+6tan(x)=8 ?

The general solution for sec^2(x)+6tan(x)=8 is x= pi/4+pin,x=-1.42889…+pin

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sec^2(x)+6tan(x)=8

sec^{2} (x) + 6 tan (x) = 8

x = \frac{π}{4} + πn, x = - 1.42889 \dots + πn

Solution steps

sec^{2} (x) + 6 tan (x) = 8

Subtract

8

from both sides

sec^{2} (x) + 6 tan (x) - 8 = 0

Rewrite using trig identities

- 7 + tan^{2} (x) + 6 tan (x) = 0

Solve by substitution

tan (x) = 1, tan (x) = - 7

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 7 : x = arctan (- 7) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (- 7) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = - 1.42889 \dots + πn

tan (θ) = - \frac{3}{8}

i, arcsin (sin (x)) = x - 2 π

3 cos (2 θ) + 13 cos (θ) + 5 = 6 cos (θ)

tan (θ) = - \frac{3}{5}

cos (x + \frac{π}{3}) + cos (x - \frac{π}{3}) = 1

What is the general solution for sec^2(x)+6tan(x)=8 ?
The general solution for sec^2(x)+6tan(x)=8 is x= pi/4+pin,x=-1.42889…+pin