What is the general solution for cos(x)cot(x)-3(1-sin(x))=0 ?

The general solution for cos(x)cot(x)-3(1-sin(x))=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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cos(x)cot(x)-3(1-sin(x))=0

cos (x) cot (x) - 3 (1 - sin (x)) = 0

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

cos (x) cot (x) - 3 (1 - sin (x)) = 0

Rewrite using trig identities

- 3 + \frac{1 + 2 sin ^{2} ( x )}{sin ( x )} = 0

Solve by substitution

sin (x) = 1, sin (x) = \frac{1}{2}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

18 = \frac{1}{2} \cdot 9 \cdot 5 \cdot sin (θ)

2 cos^{2} (x) = cos^{2} (x)

sin (\frac{π x}{2}) = 0

sin (x) = \frac{1}{2} 2

8 cos (2 x) = 2 sin (x) + 7

What is the general solution for cos(x)cot(x)-3(1-sin(x))=0 ?
The general solution for cos(x)cot(x)-3(1-sin(x))=0 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin