Question

5. Determine whether the equation below represents a valid identity and state which type of formula justifies each step. tan u + cot u ? sec u ? csc u Left hand side | Property: = tan u + cot u | Given = sin u / cos u + cos u / sin u | by using a reciprocal identity = (sin^2 u + cos^2 u) / (cos u ? sin u) | by using common denominators = 1 / (cos u ? sin u) | by using a reciprocal identity = 1 / cos u ? 1 / sin u = sec u ? csc u | by using a reciprocal identity = right hand side | Therefore, the given equation [ Select ] a valid identity.

          5. Determine whether the equation below represents a valid identity and state which type of formula justifies each step.
tan u + cot u ? sec u ? csc u

Left hand side | Property:
= tan u + cot u | Given
= sin u / cos u + cos u / sin u | by using a reciprocal identity
= (sin^2 u + cos^2 u) / (cos u ? sin u) | by using common denominators
= 1 / (cos u ? sin u) | by using a reciprocal identity
= 1 / cos u ? 1 / sin u = sec u ? csc u | by using a reciprocal identity
= right hand side | Therefore, the given equation [ Select ] a valid identity.

5. Determine whether the equation below represents a valid identity and state which type of formula justifies each step.
tan u + cot u ? sec u ? csc u

Left hand side | Property:
= tan u + cot u | Given
= sin u / cos u + cos u / sin u | by using a reciprocal identity
= (sin^2 u + cos^2 u) / (cos u ? sin u) | by using common denominators
= 1 / (cos u ? sin u) | by using a reciprocal identity
= 1 / cos u ? 1 / sin u = sec u ? csc u | by using a reciprocal identity
= right hand side | Therefore, the given equation [ Select ] a valid identity.

Added by Victor R.

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