H E L P- INCONSISTENT MATH LOGIC - How can this be?

If we know that: Sin^2 x + Cos^2 x = 1 Trig. Identity
Then Sin^2 x = 1 - Cos^2 x
(Sin^2 x)^3/2 = (1 - Cos^2 x)^3/2
Sin^3 x = (1 - Cos^2 x)^3/2
(Sin^3 x) + 1 = (1 - Cos^2 x)^3/2) + 1
Now Let x = 90 degrees or 3.14/2 radiants, then Sin 90 =1 and Cos 90 =0
(1)^3 + 1 = [1 - Cos^2(90)]^3/2 + 1
1 + 1 =(1)^3/2 + 1
2 = [(1)^3]^1/2 + 1
2 = (1)^1/2 + 1
2 = positive or negative 1 + 1
Here we have two possible answers: A) 2 = positive 1 + 1 = 2 => 2 = 2 which is true.
B) 2 = negative 1 + 1 = 0 => 2 = 0 which is not true.
Now add 2 to B) and we get 2 + 2 = 0 + 2 and that states 4 = 2 which is not true.
Now add -1 to B) and we get -1 + 2 = -1 + 0 and that states 1 = -1 which is not true.

WE CAN GO FURTHER YET:

Multiply B) by "N" where N is an element of the Reals or Complex numbers then we get the following: 2(N) = 0(N) now lets say that "N" = 9 then this implies that 18 = 9 which is not true.

OR if "N" = x real + Y imaginary then 2(x real) + 2 (y imaginary) = 0 then we can say that "X" = "Y" (only because Imaginary is equal to the square root of negative 1 by definition) Which this statement is not true.

If X is an element of the Reals, and Y is an element of the reals. Suppose x = y = 2 from B) above we have: 2(2) + 2(2) imaginary = 0 implies 4 + 4imaginary or 4(1 + imaginary) = 0 which implies that 1 + imaginary = 0 and therefore imaginary = - 1 which is not true.
Because imaginary is equal to the square root of negative 1 by definition.

NOTE where ever you see the word imaginary this is the letter "eye"


My Question is Can Someone Explain Why This Is Incorrect Math Logic?