What is the general solution for 4=tan^2(45+x/2) ?

The general solution for 4=tan^2(45+x/2) is x=2*1.10714…+360n-90,x=-2*1.10714…+360n-90

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

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

x = 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}

Solution steps

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

Switch sides

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

Solve by substitution

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

tan (4 5^{\circ} + \frac{x}{2}) = 2 : x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 2 : x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

Combine all the solutions

x = 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 arctan (2) + 36 0^{\circ} n - 9 0^{\circ}

Show solutions in decimal form

x = 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 1.10714 \dots + 36 0^{\circ} n - 9 0^{\circ}

2 sin (5 x) - 1 = 0

cos (x) = \frac{2.3}{2.8}

3000 = 5000 [cos (\frac{π}{45} (t - 6))]

2 + cos (θ) = 5 cos (θ)

11 = 12 + 3.1 cos (\frac{2 π}{365} t)

What is the general solution for 4=tan^2(45+x/2) ?
The general solution for 4=tan^2(45+x/2) is x=2*1.10714…+360n-90,x=-2*1.10714…+360n-90