Q61 / 160 · AP EAMCET 2021 (24 Aug Shift 2) · Mathematics

If $\sin \theta+\operatorname{cosec} \theta=2$, then the value of $\sin ^{10} \theta+\operatorname{cosec}^{10} \theta$ is equal to

  • Correct answer
    A
    $2$
  • B
    $2^{10}$
  • C
    $2^9$
  • D
    $2^8$

Solution

Given, $\sin \theta+\operatorname{cosec} \theta=2$ It is possible only $\sin \theta=\operatorname{cosec} \theta=1$ $\therefore \sin ^{10} \theta+\operatorname{cosec}^{10} \theta=(1)^{10}+(1)^{10}=1+1=2$

Hence, the correct answer is option: 'A'.

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