Prove that: `((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n={2cot^n((A-B)/2),ifni se v e n0,ifni sod d,`

Explanation

Given,

`((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n`


`=>((2cos((A+B)/2)​cos((A−B)/2)​​)/(2cos((A+B)/2)​ sin((A−B)/2)))^n+((2sin((A+B)/2)​cos((A−B)/2)​​)/(2sin((A+B)/2)​sin((B−A​)/2)))^n`

`=>(cot((A−B​)/2))^n+(−cot((A−B)/2)​)^n`

`=>cot^n((A−B)/2)​+(−1)^ncot^n((A−B)/2)​=cot^n
((A−B​)/2)[1+(−1)^n]`

`=0,` if n is odd

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