The value of cos⁡(π)/(2^2)⋅cos⁡(π)/(2^3)⋅…⋅cos⁡(π)/(2^10)⋅sin⁡(π)/(2^10) is

Question

The value of cos⁡(π)/(2^2)⋅cos⁡(π)/(2^3)⋅…⋅cos⁡(π)/(2^10)⋅sin⁡(π)/(2^10) is:

MARKS Content Team · Accepted Answer

Correct answer: (B) 1/512. Given cos(π2^2·cosπ2^3·...·cosπ2^10·sinπ2^10=sin2^9.π2^102^9.sinπ2^10.sinπ2^10Using cosA.cos)/(2A.cos2^2A.cos2^3A.cos2^4A.....cos2^(n-1)A=sin2^nA2^nsinA=12^9=1512)

The value of $\cos \frac{π}{2^{2}} \cdot \cos \frac{π}{2^{3}} \cdot \dots \cdot \cos \frac{π}{2^{10}} \cdot \sin \frac{π}{2^{10}}$ is:

Solution

More Trigonometric Ratios & Identities Questions

The value of cos⁡π22⋅cos⁡π23⋅…⋅cos⁡π210⋅sin⁡π210 is:

Solution

More Trigonometric Ratios & Identities Questions

The value of $\cos \frac{π}{2^{2}} \cdot \cos \frac{π}{2^{3}} \cdot \dots \cdot \cos \frac{π}{2^{10}} \cdot \sin \frac{π}{2^{10}}$ is: