Answer:
Step-by-step explanation:
(cos7A + cos3A - cos5A - cosA)÷(sin7A - sin3A - sin5a + sinA)
By using transformations,
[(cos7A - cos5A) + (cos3A - cosA)]÷[(sin7A - sin5A) - (sin3A - sinA)]....
we get...
=[(2sin6A.sinA)+(2sin2A.sinA)]÷[(2cos6A.sinA)-(2cos2A.sinA)]...
=[{2sinA(sin6A+sin2A)}]÷[{2sinA(cos6A-cos2A)]
=[{2sin4A.cos2A}÷{2sin4A.sin2A}]
=[(cos2A)÷(sin2A)]
=cot2A
