What is the general solution for 270=69-tan(45+(x/2)) ?

The general solution for 270=69-tan(45+(x/2)) is x=-2*1.56582…+360n-90

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270=69-tan(45+(x/2))

270 = 69 - tan (4 5^{\circ} + (\frac{x}{2}))

x = - 2 \cdot 1.56582 \dots + 36 0^{\circ} n - 9 0^{\circ}

Solution steps

270 = 69 - tan (4 5^{\circ} + (\frac{x}{2}))

Switch sides

69 - tan (4 5^{\circ} + \frac{x}{2}) = 270

Move

69

to the right side

- tan (4 5^{\circ} + \frac{x}{2}) = 201

Divide both sides by

- 1

tan (4 5^{\circ} + \frac{x}{2}) = - 201

Apply trig inverse properties

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

Solve

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n : x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

Show solutions in decimal form

x = - 2 \cdot 1.56582 \dots + 36 0^{\circ} n - 9 0^{\circ}

tan (x) = - \frac{8}{15}

arcsin (\frac{4}{5}) = sin (x)

4 sin^{2} (x - 6 0^{\circ}) = 3

cos (a) = - \frac{4}{5}, 9 0^{\circ} < a < 18 0^{\circ}

3 cot^{2} (2 x - \frac{3 π}{2}) = 1

What is the general solution for 270=69-tan(45+(x/2)) ?
The general solution for 270=69-tan(45+(x/2)) is x=-2*1.56582…+360n-90