If sin x + cosec X = 2, then find the value of sin^10 x + cosec^10x.​

Question

If sin x + cosec X = 2, then find the value of sin^10 x + cosec^10x.​

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Charlie 1 week 2021-09-11T05:29:12+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-11T05:30:22+00:00

    Answer:

    1024 is the answer.

    We have to find the value of 2 power 10

    0
    2021-09-11T05:31:05+00:00

    Answer:

      { \sin(x) }^{10}  +  { \csc(x) }^{10}  = 2

    Explanation :

    Given,

     \sin(x)  +  \csc(x)  = 2  \\  \\    \implies \sin(x)  +  \frac{1}{ \sin(x) }  = 2

    This is only possible when  \sin(x)\:=\:1\:or\:-1

    Therefore,

      { \sin(x) }^{10}  +  { \csc(x) }^{10}   \\  \\  =   { \sin(x) }^{10} +  \frac{1}{{ \sin(x) }^{10} } \\  \\   =  {1}^{10}  +  \frac{1}{ {1}^{10} }  = 2

    Important concept

    Whenever we come across such equations where  x^2\:+\:\dfrac{1}{x^2}\:=\:2 ,There is only when possible case where x = 1 or x = -1.

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