What is the general solution for tan^2(45+(x/2))=4.137131 ?

The general solution for tan^2(45+(x/2))=4.137131 is No Solution for x\in\mathbb{R}

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tan^2(45+(x/2))=4.137131

tan^{2} (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

No Solution for x \in R

Solution steps

tan^{2} (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

Solve by substitution

tan^{2} (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

Let:

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = u

u^{2} = 4.137131

u^{2} = 4.137131 : u = 4.137131, u = - 4.137131

u^{2} = 4.137131

For

x^{2} = f (a)

the solutions are

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

u = 4.137131, u = - 4.137131

Substitute back

u = tan (4 5^{\circ} + (\frac{x}{2})^{\circ})

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131, tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131, tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131 :

No Solution

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

Apply trig inverse properties

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

General solutions for

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (4.137131) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (4.137131) + 18 0^{\circ} n

No Solution

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131 :

No Solution

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

Apply trig inverse properties

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

General solutions for

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (- 4.137131) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (- 4.137131) + 18 0^{\circ} n

No Solution

Combine all the solutions

No Solution for x \in R

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What is the general solution for tan^2(45+(x/2))=4.137131 ?
The general solution for tan^2(45+(x/2))=4.137131 is No Solution for x\in\mathbb{R}