What is the general solution for (1+csc(A))(1-csc(A))=-cot(A) ?

The general solution for (1+csc(A))(1-csc(A))=-cot(A) is A= pi/2+pin,A= pi/4+pin

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(1+csc(A))(1-csc(A))=-cot(A)

(1 + csc (A)) (1 - csc (A)) = - cot (A)

A = \frac{π}{2} + πn, A = \frac{π}{4} + πn

Solution steps

(1 + csc (A)) (1 - csc (A)) = - cot (A)

Subtract

- cot (A)

from both sides

(1 + csc (A)) (1 - csc (A)) + cot (A) = 0

Rewrite using trig identities

cot (A) - cot^{2} (A) = 0

Solve by substitution

cot (A) = 0, cot (A) = 1

cot (A) = 0 : A = \frac{π}{2} + πn

cot (A) = 1 : A = \frac{π}{4} + πn

Combine all the solutions

A = \frac{π}{2} + πn, A = \frac{π}{4} + πn

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

cos (2 x) - 3 cos (x) + 1 = 0

2 cos^{2} (x) - cos (x) - 1 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

θ, x = tan (θ)

sin (5 X) \cdot cos (5 X) = 1

What is the general solution for (1+csc(A))(1-csc(A))=-cot(A) ?
The general solution for (1+csc(A))(1-csc(A))=-cot(A) is A= pi/2+pin,A= pi/4+pin