prove that sin²a + sin²(a-b)-2sin a cos b sin(a-b)=sin²b
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Step-by-step explanation:
LHS = sin²a + sin²(a-b)-2sin a cos b sin(a-b)
= sin²a + (sin a cos b - cos a sin b )²-2sin a cos b (sin a cos b - cos a sin b)
= sin²a + sin²a cos²b + sin²b cos²a - 2 sin a cos b cos a sin b - 2 sin a cos b sin a cos b + 2 sin a cos b cos a sin b
= sin²a + sin²a cos²b + sin²b cos²a - 2 sin a cos b sin a cos b
= sin²a + sin²(b-a)
= sin²(a + b - a)
= sin²b
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