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If asin θ + bcos θ = c, then prove that acos 0-bsin θ = Va 2 + b 2-c2 |
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Answer» Acosx - bsinx = c ------(1) take square both sides a²cos²x + b²sin²x -2absinx.cosx = c² ----(1) asinx + bcosx = L --------(2) take square both sides a²sin²x + b²cos²x +2absinx.cosx = L² ----(2) add equations (1)and (2) a²(sin²x + cos²x ) + b²( sin²x + cos²x ) = c² + L² a² + b² = c² + L² L² = a² + b² -c² L = ±√( a² + b² - c²) asinx + bcosx =±√(a² + b² - c²) |
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