What is the general solution for tan^2(x)-7tan(x)-8=0 ?

The general solution for tan^2(x)-7tan(x)-8=0 is x=1.44644…+pin,x=(3pi)/4+pin

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tan^2(x)-7tan(x)-8=0

tan^{2} (x) - 7 tan (x) - 8 = 0

x = 1.44644 \dots + πn, x = \frac{3 π}{4} + πn

Solution steps

tan^{2} (x) - 7 tan (x) - 8 = 0

Solve by substitution

tan (x) = 8, tan (x) = - 1

tan (x) = 8 : x = arctan (8) + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = arctan (8) + πn, x = \frac{3 π}{4} + πn

Show solutions in decimal form

x = 1.44644 \dots + πn, x = \frac{3 π}{4} + πn

5 tan (x) sin (x) = - 7 sin (x)

tan (x + π) - cos (x + \frac{π}{2}) = 0

2 cos^{2} (θ) - 9 cos (θ) + 4 = 0

cos (2 x + \frac{π}{4}) = \frac{2}{2}

x, tan (x) = 1

What is the general solution for tan^2(x)-7tan(x)-8=0 ?
The general solution for tan^2(x)-7tan(x)-8=0 is x=1.44644…+pin,x=(3pi)/4+pin