What is the general solution for 4tan^2(x)+21tan(x)-49=0 ?

The general solution for 4tan^2(x)+21tan(x)-49=0 is x=1.05165…+pin,x=-1.42889…+pin

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4tan^2(x)+21tan(x)-49=0

4 tan^{2} (x) + 21 tan (x) - 49 = 0

x = 1.05165 \dots + πn, x = - 1.42889 \dots + πn

Solution steps

4 tan^{2} (x) + 21 tan (x) - 49 = 0

Solve by substitution

tan (x) = \frac{7}{4}, tan (x) = - 7

tan (x) = \frac{7}{4} : x = arctan (\frac{7}{4}) + πn

tan (x) = - 7 : x = arctan (- 7) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 1.05165 \dots + πn, x = - 1.42889 \dots + πn

cot (x) = csc (x) + 1

\frac{sin ( 8 )}{30} = \frac{sin ( x )}{120}

2 sin (2 x + 1 5^{\circ}) = 1

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

tan (x) + 3 = sec (x)

What is the general solution for 4tan^2(x)+21tan(x)-49=0 ?
The general solution for 4tan^2(x)+21tan(x)-49=0 is x=1.05165…+pin,x=-1.42889…+pin