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GATE BT 2024 | Question: 19

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The value of the series $1+\sin x+\cos ^{2} x+\sin ^{3} x+\cdots$ at $x=\frac{\pi}{4}$ is $\_\_\_\_\_\_\_$.

  1. $\frac{1}{\sqrt{2}+1}$
  2. $\frac{\sqrt{2}}{\sqrt{2}+1}$
  3. $\frac{1}{\sqrt{2}-1}$
  4. $\frac{\sqrt{2}}{\sqrt{2}-1}$

     

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