find the genearal solution of the following equation 4csc^2x-7=cotx

Answer 1

since csc^2 = 1+cot^2,

4(1+cot^2x)-7 = cotx
4+4cot^2x-7 = cotx
4cot^2x - cotx - 3 = 0
(4cotx+3)(cotx-1) = 0

Now it's easy, right?

Answer 2

(4cotx+3)(cotx-1) = 0

i reached this point i need to know how to find the angles

Answer 3

oh come on. either

4cotx+3 = 0
cotx = -3/4

or

cotx-1 = 0
cotx = 1

In the first case, x will be in QII or QIV
on the second case, x will be in QI or QIII