What is the general solution for 2tan^2(x)=15 ?

The general solution for 2tan^2(x)=15 is x=1.22069…+pin,x=-1.22069…+pin

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2tan^2(x)=15

2 tan^{2} (x) = 15

x = 1.22069 \dots + πn, x = - 1.22069 \dots + πn

Degrees

x = 69.94041 \dots^{\circ} + 18 0^{\circ} n, x = - 69.94041 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 tan^{2} (x) = 15

Solve by substitution

2 tan^{2} (x) = 15

Let:

tan (x) = u

2 u^{2} = 15

2 u^{2} = 15 : u = \frac{15}{2}, u = - \frac{15}{2}

2 u^{2} = 15

Divide both sides by

2

2 u^{2} = 15

Divide both sides by

2

\frac{2 u ^{2}}{2} = \frac{15}{2}

Simplify

u^{2} = \frac{15}{2}

u^{2} = \frac{15}{2}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = \frac{15}{2}, u = - \frac{15}{2}

Substitute back

u = tan (x)

tan (x) = \frac{15}{2}, tan (x) = - \frac{15}{2}

tan (x) = \frac{15}{2}, tan (x) = - \frac{15}{2}

tan (x) = \frac{15}{2} : x = arctan (\frac{15}{2}) + πn

tan (x) = \frac{15}{2}

Apply trig inverse properties

tan (x) = \frac{15}{2}

General solutions for

tan (x) = \frac{15}{2}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{15}{2}) + πn

x = arctan (\frac{15}{2}) + πn

tan (x) = - \frac{15}{2} : x = arctan (- \frac{15}{2}) + πn

tan (x) = - \frac{15}{2}

Apply trig inverse properties

tan (x) = - \frac{15}{2}

General solutions for

tan (x) = - \frac{15}{2}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{15}{2}) + πn

x = arctan (- \frac{15}{2}) + πn

Combine all the solutions

x = arctan (\frac{15}{2}) + πn, x = arctan (- \frac{15}{2}) + πn

Show solutions in decimal form

x = 1.22069 \dots + πn, x = - 1.22069 \dots + πn

1 - cos (θ) = 1 + cos (θ)

cos (2 x) + cos (x) = 1

tan (x) sec (x) = - 2 tan (x)

1 + sin^{2} (x) = 2

sin (\frac{3 π}{2} + x) + sin (\frac{3 π}{2} + x) = - 2

What is the general solution for 2tan^2(x)=15 ?
The general solution for 2tan^2(x)=15 is x=1.22069…+pin,x=-1.22069…+pin