What is the general solution for tan(2x-30)cot(50)=1 ?

The general solution for tan(2x-30)cot(50)=1 is x=(180n)/2+40

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tan(2x-30)cot(50)=1

tan (2 x - 3 0^{\circ}) cot (5 0^{\circ}) = 1

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

Solution steps

tan (2 x - 3 0^{\circ}) cot (5 0^{\circ}) = 1

Divide both sides by

cot (5 0^{\circ})

tan (2 x - 3 0^{\circ}) = \frac{1}{cot ( 5 0 ^{\circ} )}

Apply trig inverse properties

2 x - 3 0^{\circ} = arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n

Solve

2 x - 3 0^{\circ} = arctan (\frac{1}{cot ( 5 0 ^{\circ} )}) + 18 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

x = \frac{18 0 ^{\circ} n}{2} + 4 0^{\circ}

x, 3 sec^{4} (x) - 10 sec^{2} (x) + 8 = 0

4 (1 + sin (x)) sin (x) = 3

tan (x^{\circ}) = 0.57

3 sin (x) - 2 = 7 sin (x) - 3

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 \cdot cos (x)

What is the general solution for tan(2x-30)cot(50)=1 ?
The general solution for tan(2x-30)cot(50)=1 is x=(180n)/2+40