What is the general solution for 3sec^2(x)+tan(x)-6=0 ?

The general solution for 3sec^2(x)+tan(x)-6=0 is x=0.70282…+pin,x=-0.86797…+pin

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

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

x = 0.70282 \dots + πn, x = - 0.86797 \dots + πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{- 1 + 37}{6}, tan (x) = \frac{- 1 - 37}{6}

tan (x) = \frac{- 1 + 37}{6} : x = arctan (\frac{- 1 + 37}{6}) + πn

tan (x) = \frac{- 1 - 37}{6} : x = arctan (\frac{- 1 - 37}{6}) + πn

Combine all the solutions

x = arctan (\frac{- 1 + 37}{6}) + πn, x = arctan (\frac{- 1 - 37}{6}) + πn

Show solutions in decimal form

x = 0.70282 \dots + πn, x = - 0.86797 \dots + πn

2 sin (x) + cot (x) = csc (x)

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

cos (A) = \frac{1}{65}, cos (B) = \frac{1}{5}

sin (θ) = 0.9063

a \cdot sin (x) + b \cdot cos (x) = 0

What is the general solution for 3sec^2(x)+tan(x)-6=0 ?
The general solution for 3sec^2(x)+tan(x)-6=0 is x=0.70282…+pin,x=-0.86797…+pin