15 points McKTrig8 51023 Prove that the following identity

+ 15 points McKTrig8 5.1.023 Prove that the following identity is true. sin2x (cot2 x + 1) = 1

Solution

We have given sin²x(cot²x+1)=1

sin²x(cot²x+1)=1

sin²x*cot²x+sin²x=1

plug cot²x=cos²x/sin²x into above equation

sin²x*(cos²x/sin²x)+sin²x=1

cos²x+sin²x=1

1=1 since we know that sin²x+cos²x=1

LHS=RHS

so the given identity is true.