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=-540n+135-3*0.65086…,x=-540n+135+3*0.65086…

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

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

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

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 = - 54 0^{\circ} n + 13 5^{\circ} - 3 arctan (0.58)

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

Combine all the solutions

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

Show solutions in decimal form

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

- 20 csc (x) = 40

0 = 4 ∣ sin (6 θ) ∣

5 sin^{2} (θ) - 11 sin (θ) + 6 = 0

cos (x) = \frac{11}{14}, sin (x)

sin^{2} (2 x) + cos^{2} (3 x) = 1

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=-540n+135-3*0.65086…,x=-540n+135+3*0.65086…