Question

the expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps: step 1: secant x over tangent x plus 1 over tangent x step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x step 4: 1 over sine x plus cosine x over sine x step 5: cosecant x plus cosine x over sine x step 6: cosecant x plus cotangent x which identity/formula was used to simplify from step 4 to step 5?

Answer 1

The identity/formula used to simplify from step 4 to step 5 is the reciprocal identity for sine, which states that 1/sin(x) = csc(x).

Step-by-step explanation:

The identity/formula used to simplify from step 4 to step 5 is the reciprocal identity for sine:

1/sin(x) = csc(x)

Using this identity, we can rewrite the expression in step 4 as cosecant(x) + cosine(x)/sin(x), which simplifies to cosecant(x) + cotangent(x) in step 5.