6. Prove the identity. cos2x-1 tan x sin x COS X To prove the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step. 2 COS x-1 COS X (1) COS X =-tan x sin x (2). O Cancel common factors. Apply a reciprocal identity. Apply a Pythagorean identity. Apply a quotient identity. (2) OOOO Divide out the common factor and then use a quotient identity. Use a reciprocal identity. Divide out the common factor and then use a reciprocal identity. O Use a quotient identity. 7. Prove that the following equation is an identity. 1-2 sin x cos x = (sin x cos x) 1-2 sin x cos x = (sin x cos x) = = = 1-2 sin x cos x FOIL right-hand side. Rearrange terms on right hand side by swapping the middle and last term. Use a Pythagorean Identity on the first two terms. 8. Verify the identity. 1 csc x-cot x 1 csc x + cot x 2 sin x Choose the sequence of steps below that verifies the identity. A. 1 1 CSC x + cot x CSC x-cot x csc x + cot x+ csc x- cot x (csc x+ cot x)(csc x-cot x) CSC 2 csc x 2 2 x + cotx = 2 cot x 2 sin x B. 1 1 csc x-cot x csc x + cot x csc x+ cot x+ csc x-cot x (csc x+ cot x)(csc x- cot x) 2 csc x 2 csc x- cot x = 2 cot x = 2 sin x C. csc x+cot x CSC x-cot x csc x+ cot x+ csc x- cot x = (csc x+ cot x)(csc x- cot x) 2 csc x 2 CSC X- cot 2 x = 2 csc x 2 sin x