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Vijay Rao Palla
Asked: 2022-10-29T19:18:38+05:30 In:

If a SinA + b cosA = c, then a cosA – b sinA is equal to:
1. \(\sqrt {{a^2} + {b^2} + {c^2}}\)
2. \(\sqrt {{a^2} – {b^2} + {c^2}}\)
3. \(\sqrt {{a^2} + {b^2} – {c^2}}\)
4. \(\sqrt {{a^2} – {b^2} – {c^2}}\)

If a SinA + b cosA = c, then a cosA – b sinA is equal to:
1. \(\sqrt {{a^2} + {b^2} + {c^2}}\)
2. \(\sqrt {{a^2} – {b^2} + {c^2}}\)
3. \(\sqrt {{a^2} + {b^2} – {c^2}}\)
4. \(\sqrt {{a^2} – {b^2} – {c^2}}\)
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1 Answer

  1. Correct Answer – Option 3 : \(\sqrt {{a^2} + {b^2} – {c^2}}\)

    GIven:

    a SinA + b cosA = c

    Formula used:

    If a Sinθ + b Cosθ = c

    Then, a Cosθ – b Sinθ = \(\sqrt {{a^2} + {b^2} – {c^2}}\)

    Calculation:

    Apply above formula on a SinA + b cosA = c 

    We get

    ⇒ a CosA – b SinA = \(\sqrt {{a^2} + {b^2} – {c^2}}\)

    ∴ a CosA – b SinA is equla to  \(\sqrt {{a^2} + {b^2} – {c^2}}\)

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