What is the general solution for tan^2(45+x/3)=0.58 ?

The general solution for tan^2(45+x/3)=0.58 is x=3*0.65086…+540n-135,x=-3*0.65086…+540n-135

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tan^2(45+x/3)=0.58

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

x = 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}

Solution steps

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

Solve by substitution

tan (4 5^{\circ} + \frac{x}{3}) = 0.58, tan (4 5^{\circ} + \frac{x}{3}) = - 0.58

tan (4 5^{\circ} + \frac{x}{3}) = 0.58 : x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}

tan (4 5^{\circ} + \frac{x}{3}) = - 0.58 : x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

Combine all the solutions

x = 3 arctan (0.58) + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 arctan (\frac{29}{5 2}) + 54 0^{\circ} n - 13 5^{\circ}

Show solutions in decimal form

x = 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}, x = - 3 \cdot 0.65086 \dots + 54 0^{\circ} n - 13 5^{\circ}

1 = 4 cos^{2} (x) - 4 cos (x) + 2

1 = cos (3 θ)

3 sin (2 x) + cos (x) = 0

sinh (a x) = 0

8 sin^{4} (x) - 3 sin^{2} (x) + \frac{1}{4} = 0

What is the general solution for tan^2(45+x/3)=0.58 ?
The general solution for tan^2(45+x/3)=0.58 is x=3*0.65086…+540n-135,x=-3*0.65086…+540n-135