What is the general solution for tan(2x+10)=1.5 ?

The general solution for tan(2x+10)=1.5 is x=(180n)/2+(0.98279…)/2-5

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tan(2x+10)=1.5

tan (2 x + 1 0^{\circ}) = 1.5

x = \frac{18 0 ^{\circ} n}{2} + \frac{0.98279 \dots}{2} - 5^{\circ}

Solution steps

tan (2 x + 1 0^{\circ}) = 1.5

Apply trig inverse properties

2 x + 1 0^{\circ} = arctan (1.5) + 18 0^{\circ} n

Solve

2 x + 1 0^{\circ} = arctan (1.5) + 18 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{2} + \frac{arctan ( 1.5 )}{2} - 5^{\circ}

x = \frac{18 0 ^{\circ} n}{2} + \frac{arctan ( 1.5 )}{2} - 5^{\circ}

Show solutions in decimal form

x = \frac{18 0 ^{\circ} n}{2} + \frac{0.98279 \dots}{2} - 5^{\circ}

- 5 sec^{2} (x) - 10 sec (x) = - 15

tan (x + 2 0^{\circ}) = cot (x)

2 sin (θ) = cot (θ)

3 csc^{2} (x) + 1 = 5

6 cos^{2} (x) - 12 cos (x) + 6 = 0

What is the general solution for tan(2x+10)=1.5 ?
The general solution for tan(2x+10)=1.5 is x=(180n)/2+(0.98279…)/2-5