What is the general solution for 1715/70 =tan(45+θ/2) ?

The general solution for 1715/70 =tan(45+θ/2) is θ=2*1.53000…+360n-90

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1715/70 =tan(45+θ/2)

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

Solution steps

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

Switch sides

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{1715}{70}

Cancel the common factor:

35

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

Apply trig inverse properties

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

Solve

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n : θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

Show solutions in decimal form

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

sin (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}

cos (3 x) = sin (x - 3 0^{\circ})

4 sin (θ) = 4 cos (2 θ)

tan (5 θ + 30) = 1

885 cos (θ) - 70 = cos (25 0^{\circ})

What is the general solution for 1715/70 =tan(45+θ/2) ?
The general solution for 1715/70 =tan(45+θ/2) is θ=2*1.53000…+360n-90