JEE Mains · Maths · STD 11 - 8. sequence and series
The value of \(\cos \,\frac{\pi }{{{2^2}}}.\cos \,\frac{\pi }{{{2^3}}}{._{..................}}.\cos \,\frac{\pi }{{{2^{10}}}}.\,\sin \,\frac{\pi }{{{2^{10}}}}\) is
- A \(\frac{1}{512}\)
- B \(\frac{1}{1024}\)
- C \(\frac{1}{256}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{512}\)
Step-by-step Solution
Detailed explanation
Using formula \(\frac{{\sin \,{2^n}\,A}}{{{2^n}\sin \,A}} = cos\,A\,cos\,2A\,cos\,2^2 A...........cos\,2^{n-1} A\)
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