Verify the identity algebraically. Use a graphing utility to check your result graphically.

Question

5cot(𝛼) / csc(𝛼) - 1 =5csc(𝛼) + 5 / cot(𝛼)

Multiply the numerator and denominator by a common expression, and then use a Pythagorean Identity to simplify. (Simplify your answers completely.)

5cot(𝛼) / csc(𝛼) - 1 = 5cot(𝛼) / csc(𝛼) - 1 ✕ csc(𝛼) + 1 / ______ =

(5 cot(𝛼))(csc(𝛼) + 1) / ________

= ______ / cot(𝛼)

Answer 1

5cot(α) (csc(α) + 1)/((csc(α)-1)(csc(α)+1) = 5cot(α)(csc(α) + 1)/(csc²(α)-1)

= 5cot(α)(csc(α) + 1)/cot²(α) = 5(csc(α)+1)/cot(α) = (5csc(α)+5)/cot(α)