What is the general solution for 6sec^2(x)+tan(x)-9=0 ?

The general solution for 6sec^2(x)+tan(x)-9=0 is x=0.56123…+pin,x=-0.67188…+pin

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6sec^2(x)+tan(x)-9=0

6 sec^{2} (x) + tan (x) - 9 = 0

x = 0.56123 \dots + πn, x = - 0.67188 \dots + πn

Solution steps

6 sec^{2} (x) + tan (x) - 9 = 0

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{- 1 + 73}{12}, tan (x) = \frac{- 1 - 73}{12}

tan (x) = \frac{- 1 + 73}{12} : x = arctan (\frac{- 1 + 73}{12}) + πn

tan (x) = \frac{- 1 - 73}{12} : x = arctan (\frac{- 1 - 73}{12}) + πn

Combine all the solutions

x = arctan (\frac{- 1 + 73}{12}) + πn, x = arctan (\frac{- 1 - 73}{12}) + πn

Show solutions in decimal form

x = 0.56123 \dots + πn, x = - 0.67188 \dots + πn

3 tan^{2} (x) - cos^{2} (x) = sin^{2} (x)

cos (θ) = \frac{2 π}{3}

3 (tan (θ) - 2) = 2 tan (- 7)

4 cos^{2} (x) + 7 cos (x) = 2

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

What is the general solution for 6sec^2(x)+tan(x)-9=0 ?
The general solution for 6sec^2(x)+tan(x)-9=0 is x=0.56123…+pin,x=-0.67188…+pin