Acosx-Bsinx=C prove that Asinx+Bcosx= root of(A^2+B^2-C^2)
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Step-by-step explanation:
Acosx-Bsinx=c
(Acosx-Bsinx)²=C²
A²cos²x+B²sin²x-2Acosxsinx=C²
2Asinxcosx=A²cos²x + B²sin²x -C²
(Asinx+Bcosx)² = A²sin²x+B²cos²x+2ABsinxcosx
=A²sin²x+B²cos²x+A²cos²x+B²sin²x - C²
=A²(sin²x+cos²x)+B²(sin²x+cos²x)-C²
=A²+B²-C²
Hence proved
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