Basic hyperbolic identities

Basic hyperbolic identities Quiz

Spec H6 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Given sinh⁡x=125\sinh x=\frac{12}{5}, find cosh⁡x\cosh x.

    • A. 16925\frac{169}{25}
    • B. 1195\frac{\sqrt{119}}{5}
    • C. 175\frac{17}{5}
    • D. 135\frac{13}{5}

  2. 2. Given x>0x>0 and tanh⁡x=35\tanh x=\frac35, find cosh⁡x\cosh x.

    • A. 45\frac45
    • B. 2516\frac{25}{16}
    • C. 54\frac54
    • D. 345\frac{\sqrt{34}}{5}

  3. 3. Given cosh⁡x+sinh⁡x=5\cosh x+\sinh x=5, find cosh⁡x−sinh⁡x\cosh x-\sinh x.

    • A. 55
    • B. 15\frac15
    • C. 11
    • D. −15-\frac15

  4. 4. Which identity is correct?

    • A. cosh⁡2x+sinh⁡2x=1\cosh^2x+\sinh^2x=1
    • B. sinh⁡2x−cosh⁡2x=1\sinh^2x-\cosh^2x=1
    • C. cosh⁡2x−sinh⁡2x=−1\cosh^2x-\sinh^2x=-1
    • D. cosh⁡2x−sinh⁡2x=1\cosh^2x-\sinh^2x=1

  5. 5. Which expression is equal to 1−tanh⁡2x1-\tanh^2x?

    • A. 1cosh⁡2x\frac{1}{\cosh^2x}
    • B. 1sinh⁡2x\frac{1}{\sinh^2x}
    • C. sinh⁡2xcosh⁡2x\frac{\sinh^2x}{\cosh^2x}
    • D. cosh⁡2x\cosh^2x

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