IF+COS*4/A*3+SIN*4/A=1/A=B SHOW THAT COS*8/A*3+SIN*8/B*3=1/(A+B)*3

Hello student,
I think you have missed several terms while typing your question
I am assuming the question is
If cos⁴x/a + sIn ⁴x/b = (1/a+b), then we are required to prove that
cos⁸x/a³ + sIn ⁸x/b³ = (1/a+b)³
Solution: We know that cos⁴x = (cos²x)² = (1 – sin²x)² = 1 + sin⁴x – 2sin²x
So, sin⁴x/b + cos⁴x/a = 1/(a+b)


So, cos⁸x/a³ + sIn ⁸x/b³ = (1/a+b)³