Prove that the following equation is an identity 3 cot x2

Prove that the following equation is an identity (3 + cot x)^2 - csc^2 x = 8 + 6 cot x Choose the correct answer below (3 +cot x)^2 - csc^2 x = 9 + 6 cot x + cot^2 x - csc^2 x = 9 + 6 cot x + = 8 + 6 cot x (3 +cot x)^2 - csc^2 x = 9 + 3 cot x - cot^2 x - csc^2 x = 9 + 6 cot x - 1 = 8 + 6 cot x (3 +cot x)^2 - csc^2 x = 9 + 6 cot x + cot^2 x - csc^2 x = 9 + 6 cot x - 1= 8 + 6 cot x (3 +cot x)^2 - csc^2 x = 9 + 3 cot x + cot^2 x - csc^2 x = 9 + 6 cot x + 1 = 8 + 6 cot x

Solution

given (3+cotx)^2 - csc^2x = 9+cot^2x+6cotx - csc^2x = 9 - [csc^2x - cot^2x] + 6cotx = 9 - 1 + 6cotx = 8 + 6cotx