The symbol "csc" stands for the cosecant function, which is the reciprocal of the sine function. The 2 after the symbol indicates that the function is being squared.
To solve for @, you can rearrange the equation using algebraic manipulation. First, expand the square in the denominator, then move all terms containing @ to one side of the equation. Finally, divide both sides by the remaining terms to isolate @.
Yes, the equation can be simplified by using trigonometric identities. Specifically, the identity "1-(sin@-cos@)^2 = cos^2@+sin^2@-2sin@cos@" can be used to simplify the denominator, resulting in the equation "csc2@ = 1/(cos^2@+sin^2@-2sin@cos@)."
The domain of the equation is all real numbers except when the denominator is equal to 0. This occurs when the value of @ makes the cosine function equal to 0, which happens at angles of 90 degrees, 270 degrees, etc. These values must be excluded from the domain.
To prove the identity, you can use the Pythagorean identity "cos^2@+sin^2@ = 1" and the double angle identity "2sin@cos@ = sin2@", where sin2@ is equal to 2sin@cos@. Substituting these identities into the simplified equation gives "csc2@ = 1/(1-sin2@)."