Show that sin^4x-cos^4x/sin^2x -cos^2x =1

Answer 1

(sin⁴x - cos⁴x)/(sin²x - cos²x)=1, Is this true?

using the formula: a² - b² =(a + b)(a - b)

sin⁴x - cos⁴x becomes (sin²x + cos²x) (sin²x - cos²x)

we now have

(sin²x + cos²x) (sin²x - cos²x)/(sin²x - cos²x)=1

cancel the following terms

(sin²x + cos²x) (sin²x - cos²x)/(sin²x - cos²x)=1

to get

(sin²x + cos²x)=1

Answer 2

The answer by Mr. Reno is correct. I can show at least 2 more possible solutions, but this one is the simplest. Because l am new to Wyzant, l was curious on how the students write the question using the platform, and found out that for us, experts, it's often confusing to determine, what is the question all about, especially when math notation is wrong. My suggestion to everybody: PLEASE AT FIRST TYPE IN "WORDS" THE PROBLEM AND THEN USE COPY-PASTE FEATURE OF Microsoft OFFICE TO PUT IT ON WYZANT PLATFORM.