What is the general solution for tan(2x)=0.75 ?

The general solution for tan(2x)=0.75 is x=(0.64350…)/2+(pin)/2

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tan(2x)=0.75

tan (2 x) = 0.75

x = \frac{0.64350 \dots}{2} + \frac{πn}{2}

Solution steps

tan (2 x) = 0.75

Apply trig inverse properties

2 x = arctan (0.75) + πn

Solve

2 x = arctan (0.75) + πn : x = \frac{arctan ( 0.75 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 0.75 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.64350 \dots}{2} + \frac{πn}{2}

3 tan^{2} (x) + 7 tan (x) + 4 = 0

cos (2 θ) - 3 = - 5 sin (θ)

sin (2 x) = 0

7 sin^{2} (x) + 3 cos^{2} (x) = 5

sin (x) = 0.3746

What is the general solution for tan(2x)=0.75 ?
The general solution for tan(2x)=0.75 is x=(0.64350…)/2+(pin)/2