Establish the identity. 4 cot u - tan u / cot u + tan u + 1 = 5 cos^2 u

Question

Write the left side in terms of sine and cosine.

?/? + 1 (Do not simplify.)

Write the expressions in the numerator and denominator from the previous step as single quotients with the common denominator.

?/sin u cos u / ?/sin u cos u + 1

Simplify the fraction from the previous step by canceling the common factors.

? / ? + 1

The fraction from the previous step then simplifies to 5 cos²u using what?

A. Cancellation Property (used twice).

B. Reciprocal Identity and Quotient Identity.

C. Pythagorean Identity (used twice).

D. Reciprocal Identity.

E. Cancellation Property and Pythagorean Identity.

Answer 1

(4 cot u - tan u) /(cot u + tan u) + 1 = (4cos²u - sin²u)/

(cos²U + sin²u) + 1 = 4cos²u - sin²u + 1 = 4cos²u + cos²u = 5cos²u