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Trigonometry: Maximum Value

XAT 2011 · Quantitative Ability & Data Interpretation · Easy · Trigonometry

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What is the maximum possible value of (21sin⁡X+72cos⁡X)(21 \sin X + 72 \cos X)?

  1. A.

    21

  2. B.

    57

  3. C.

    63

  4. D.

    75

  5. E.

    None of the above

Answer

D

Explanation

Maximum value of asin⁡X+bcos⁡X=a2+b2=212+722=441+5184=5625=75a \sin X + b \cos X = \sqrt{a^2 + b^2} = \sqrt{21^2 + 72^2} = \sqrt{441 + 5184} = \sqrt{5625} = 75.

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