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Prove that: (cosx-cosy)^2+(sinx-siny)^2=...

Prove that: `(cosx-cosy)^2+(sinx-siny)^2=4sin^2``(x-y)/2`

Text Solution

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LHS = `(cosx-cosy)^(2)+(sinx-siny)^(2)`
`=[2sin(x+y)/(2)sin(y-x)/(2)]^(2) + [2cos(x+y)/(2)sin(x-y)/(2)]^(2)`
`=4sin^(2)(x+y)/(2)sin^(2)(x-y)/(2)`
`=4sin^(2)(x-y)/(2)[(sin^(2)(x+y)(2)+cos^(2)(x+y)/(2))]`
`=4sin^(2)(x-y)/(2)` ................ (1)
`=4sin^(2)(x-y)/(2)`= RHS Hence Proved.
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