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The value of 

\cos\frac{\pi}{2^2}\cdot\cos\frac{\pi}{2^3}\cdot...\cdot\cos\frac{\pi}{2^{10}}\cdot\sin\frac{\pi}{2^{10}} is:

  • Option 1)

    \frac{1}{256}

  • Option 2)

    \frac{1}{2}

  • Option 3)

    \frac{1}{1024}

  • Option 4)

    \frac{1}{512}

Answers (1)

best_answer

 

Double Angle Formula -

Double angle formula

- wherein

These are formulae for double angles.

 

 

Trigonometric Ratios of Special Angles -

- wherein

These are the values of trigonometric ratios for standard angles. 

 

\cos \frac{\pi}{2^{2}}\cdot \cos \frac{\pi}{2^{3}}\cdot\cos \frac{\pi}{2^{4}}\cdot.............\cos \frac{\pi}{2^{10}}\cdot\sin \frac{\pi}{2^{10}}

=\frac{\sin (2^{9}\cdot \frac{\pi}{2^{10}})}{2^{9}\sin(\frac{\pi}{2^{10}})}\times \sin (\frac{\pi}{2^{10}})

=\frac{1}{2^{9}}\sin \frac{\pi}{2}

=\frac{1}{512}

 


Option 1)

\frac{1}{256}

Option 2)

\frac{1}{2}

Option 3)

\frac{1}{1024}

Option 4)

\frac{1}{512}
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