What is the general solution for sec^2(x)+5tan(x)=7 ?

The general solution for sec^2(x)+5tan(x)=7 is x= pi/4+pin,x=-1.40564…+pin

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sec^2(x)+5tan(x)=7

sec^{2} (x) + 5 tan (x) = 7

x = \frac{π}{4} + πn, x = - 1.40564 \dots + πn

Solution steps

sec^{2} (x) + 5 tan (x) = 7

Subtract

7

from both sides

sec^{2} (x) + 5 tan (x) - 7 = 0

Rewrite using trig identities

- 6 + tan^{2} (x) + 5 tan (x) = 0

Solve by substitution

tan (x) = 1, tan (x) = - 6

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 6 : x = arctan (- 6) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (- 6) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = - 1.40564 \dots + πn

3 sin (2 x) - 2 cos (x) = 0

sec (x) tan (x) - cos (x) cot (x) = sin (x)

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

sin (2 x) = - 5 cos (2 x)

tan (x) cot (x) = sec (x) csc (x)

What is the general solution for sec^2(x)+5tan(x)=7 ?
The general solution for sec^2(x)+5tan(x)=7 is x= pi/4+pin,x=-1.40564…+pin