Question

Which of the following expressions is equivalent to (tan u + cot u)(cos u + sin u)?

A) csc u + sec u

B) cos u + sin u

C) tan u · cot u

D) sin u · cos u

Answer 1

The equivalent expression to (tan u + cot u)(cos u + sin u) is C) tan u · cot u, which simplifies to 1, based on trigonometric identities.

Step-by-step explanation:

The student is asking which expression is equivalent to (tan u + cot u)(cos u + sin u). To find the equivalent expression, we can use trigonometric identities. The identity tan u = sin u / cos u and cot u = cos u / sin u can be used to rewrite the expression:

(sin u / cos u + cos u / sin u)(cos u + sin u) = sin2 u + cos2 u = 1 since sin2 u + cos2 u is a well-known trigonometric identity which equals 1. Therefore, the equivalent expression is option C) tan u · cot u since tan u · cot u is also equal to 1.