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If sin A = sin B and cos A = cos B, find...

If `sin A = sin B and cos A = cos B,` find all the values of A in terms of B.

Text Solution

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`sin A- sin B=0` and `cos A-cos B=0`
`rArr 2"sin" (A-B)/2 "cos" (A+B)/2=0` and `2 "sin" (A+B)/2 "sin" (B-A)/2 =0`
We observe that the common factor gives `"sin" (A-B)/2=0`. Thus,
`(A-B)/2 = npi, n in Z`
or `A-B=2n pi, n in Z`
or `A=2n pi +B, n in Z`
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