What is the general solution for 2cot(x)cos(x)+2cos(x)=cot(x)+1 ?

The general solution for 2cot(x)cos(x)+2cos(x)=cot(x)+1 is x=(3pi)/4+pin,x= pi/3+2pin,x=(5pi)/3+2pin

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2cot(x)cos(x)+2cos(x)=cot(x)+1

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

x = \frac{3 π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 cot (x) cos (x) + 2 cos (x) = cot (x) + 1

Subtract

cot (x) + 1

from both sides

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1 = 0

Factor

2 cot (x) cos (x) + 2 cos (x) - cot (x) - 1 : (cot (x) + 1) (2 cos (x) - 1)

(cot (x) + 1) (2 cos (x) - 1) = 0

Solving each part separately

cot (x) + 1 = 0 or 2 cos (x) - 1 = 0

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{3 π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan (θ) - 7 = - 12 cot (θ)

2 \cdot sin^{2} (x) - sin (x) = 1

4 cos^{2} (3 x) - 1 = 0

6 sin (b) + 12 = 0

40 + 40 cos (\frac{2 π x}{9}) = 50

What is the general solution for 2cot(x)cos(x)+2cos(x)=cot(x)+1 ?
The general solution for 2cot(x)cos(x)+2cos(x)=cot(x)+1 is x=(3pi)/4+pin,x= pi/3+2pin,x=(5pi)/3+2pin