Prove that:
`(sin5a-sin7A+sin8A-sin4a)(cos4A+cos7A-cos5A-cos8A)=cot 6A`

Explanation

LHS `((sin8A-sin4A)-(sin7A-sin5A))/((cos4A-cos8A)-(cos5A-cos7A))`
`(2cos((8A+4A)/(2)).sin((8A-4A)/(2))-2cos(7A+5A)/(2)sin(7A-5A)/(2))/(2sin(4A+8A)/(2).sin(8A-4A)/(2))`
`(2[cos6Asin2A-cos6AsinA])/(2[sin6Asin2A-sin6AsinA])`
`=(cos6A(sin2A-sinA))/(sin6A(sin2A-sinA))`
`=(cos6A)/(cos6A)=cot6A`= RHS Hence Proved.