What is the general solution for csc(x-pi)cos^2(x-pi)-cot(x-pi)=0 ?

The general solution for csc(x-pi)cos^2(x-pi)-cot(x-pi)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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csc(x-pi)cos^2(x-pi)-cot(x-pi)=0

csc (x - π) cos^{2} (x - π) - cot (x - π) = 0

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

Solution steps

csc (x - π) cos^{2} (x - π) - cot (x - π) = 0

Rewrite using trig identities

\frac{- cos ^{2} ( x ) - cos ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos^{2} (x) - cos (x) = 0

Solve by substitution

cos (x) = - 1, cos (x) = 0

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

Since the equation is undefined for:

π + 2 πn

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

tan^{2} (θ) + 6 tan (θ) + 8 = 0

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

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

sin (4 x) + 1 = 0

4 cos^{2} (θ) = 3

What is the general solution for csc(x-pi)cos^2(x-pi)-cot(x-pi)=0 ?
The general solution for csc(x-pi)cos^2(x-pi)-cot(x-pi)=0 is x= pi/2+2pin,x=(3pi)/2+2pin