What is the general solution for 189.4=100tan^2(45-x/2) ?

The general solution for 189.4=100tan^2(45-x/2) is x=-360n+90-2*0.94242…,x=-360n+90+2*0.94242…

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189.4=100tan^2(45-x/2)

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.94242 \dots, x = - 36 0^{\circ} n + 9 0^{\circ} + 2 \cdot 0.94242 \dots

Solution steps

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

Switch sides

100 tan^{2} (4 5^{\circ} - \frac{x}{2}) = 189.4

Solve by substitution

tan (4 5^{\circ} - \frac{x}{2}) = 1.894, tan (4 5^{\circ} - \frac{x}{2}) = - 1.894

tan (4 5^{\circ} - \frac{x}{2}) = 1.894 : x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894)

tan (4 5^{\circ} - \frac{x}{2}) = - 1.894 : x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

Combine all the solutions

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 arctan (1.894), x = - 36 0^{\circ} n + 9 0^{\circ} + 2 arctan (1.894)

Show solutions in decimal form

x = - 36 0^{\circ} n + 9 0^{\circ} - 2 \cdot 0.94242 \dots, x = - 36 0^{\circ} n + 9 0^{\circ} + 2 \cdot 0.94242 \dots

5 = sin (x)

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

5 sin^{2} (x) = 0

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 \cdot sin ^{2} ( x ) )}) = 0.4

cos (3 x + \frac{π}{4}) = - \frac{3}{2}

What is the general solution for 189.4=100tan^2(45-x/2) ?
The general solution for 189.4=100tan^2(45-x/2) is x=-360n+90-2*0.94242…,x=-360n+90+2*0.94242…