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Prove that : 1+(cot^(2)alpha)/(1+"cosec...

Prove that : `1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha`

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1+(cot^(2)alpha)/(1+cos ec alpha)=cos ec alpha

Show that 1+cot^2alpha/(1+cosecalpha)=cosec alpha

Knowledge Check

  • tanalpha=2 , then the value of ("cosec"^(2)alpha-sec^(2)alpha)/("cosec"^(2)alpha+sec^(2)alpha) is

    A
    `-(15)/(9)`
    B
    `-(3)/(5)`
    C
    `(3)/(5)`
    D
    `(17)/(5)`

  • The value of the integral int_(0)^(3alpha) cosec (x-alpha)cosec(x-2alpha)dx is

    A
    `2"sec" alpha log((1)/(2)"cosec" alpha)`
    B
    `2 "sec" alpha log((1)/(2)"sec "alpha)`
    C
    `2 "cosec" alpha log ("sec" alpha)`
    D
    `2 " cosec " alpha log((1)/(2)sec alpha)`

  • The simplified value of cosec^(2) alpha(1+(1)/(sec alpha))(1-(1)/(sec alpha)) is ______

    A
    1
    B
    0
    C
    2
    D
    `-1`

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