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If sqrt(1+x^(2))sintheta=x," Prove that ...

If `sqrt(1+x^(2))sintheta=x," Prove that "tan^(2)theta+cot^(2)theta=x^(2)+(1)/(x^(2)`

Text Solution

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The correct Answer is:
`thereforetan^(2)theta+cot^(2)theta=x^(2)+(1)/(x^(2)`
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Knowledge Check

  • (1+tan^(2)theta)/(1+cot^(2)theta)=

    A
    `cos^(2)theta`
    B
    `tan^(2)theta`
    C
    `sin^(2)theta`
    D
    `cot^(2)theta`

  • If sintheta=costheta then 2tan^(2)theta+sin^(2)theta-1=___ .

    A
    `(-3)/(2)`
    B
    `(3)/(2)`
    C
    `(2)/(3)`
    D
    `(-2)/(3)`

  • If tan theta+cot theta=3, then tan^(2) theta+cot^(2) theta= ____.

    A
    `4`
    B
    `7`
    C
    `6`
    D
    `9`

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