Prove that:
`(cosA+cosB)^(2)+(sinA+sinB)^(2)=4cos^(2)(A-B)/2`

Prove that: (cosA-cosB)^(2)+(sinA-sinB)^(2)=4sin^(2)(A-B)/(2)

Prove that, (cosA-cosB)^(2)+(sinA-sinB)^(2)=4sin^(2)((A-B)/(2))

Prove that (cosA-cosB)^2+(sinA-sinB)^2=4sin^2((A-B)/2)

Prove that ((cosA+cosB)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n=2cot^n((A-B)/2) or according as n is even or oddrespectively..

Prove that: ((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n={2cot^n((A-B)/2) ,if n is even, 0 if n is odd,

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,

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,

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,

If none of the denominators is zero, prove that. ((cosA+cosB)/(sinA-sinB))^(n)+((sinA-sinB)/(cosA+cosB))^(n) = {(2cot^(n)((A-B)/(2)), if n "is even"),(0, if n "is odd"):} .

Prove that ((cos A+cos B)/(sinA-sinB))^(n)+((sinA+sinB)/(cos A-cosB))^(n) =2cot^(n)""(A-B)/(2) or 0, accordingly as n is even or odd.