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For all n in N, cos theta cos 2theta cos...

For all `n in N, cos theta cos 2theta cos 4theta ....cos2^(n-1)theta` equals to

A

`(sin2^(n)theta)/(2^(n)sintheta)`

B

`(sin2^(n)theta)/(sintheta)`

C

`(cos2^(n)theta)/(2^(n)cos2theta)`

D

`(cos2^(n)theta)/(2^(n)sin2theta)`

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A
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OBJECTIVE RD SHARMA-MATHEMATICAL INDUCTION -Exercise
  1. n^(th) term of the series 4+14+30+52+ .......=

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  2. 3 + 13 + 29 + 51 + 79+… to n terms =

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  3. Sum of n terms of the following series1^3+3^3+5^3+7^3+

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  4. If 10^n+3xx4^(n+2)+lambda is divisible by 9 or all n N , then the lea...

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  5. If x^n-1 is divisible by x-k then the least positive integral value of...

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  6. If a,b are distinct rational numbers, then for all n in N the number a...

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  7. If n is an odd positive integer, then a^(n)+b^(n) is divisible by

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  8. If n is an even positive integer, then a^(n)+b^(n) is divisible by

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  9. For all n in N, (n^(5))/(5)+(n^(3))/(3)+(7)/(15n) is

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  10. The sum of n terms of the series 1+(1+a)+(1+a+a^(2))+(1+a+a^(2)+a^(...

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  11. If 3+5+9+17+33+… to n terms =2^(n+1)+n-2, then nth term of LHS, is

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  12. 7^(2n)+2^(3n-3)*3^(n-1) is divisible by 25

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  13. Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

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  14. If n in N , x^(2n-1) + y^(2n-1) is divisible by x+y if n is

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  15. The sum of the cubes of three consecutive natural numbers is divisible...

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  16. ((n+2)!)/((n-1)!) is divisible by

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  17. For all n in N, n^(4) is less than

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  18. For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

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  19. For all n in N, Sigma n

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  20. For all n in N, cos theta cos 2theta cos 4theta ....cos2^(n-1)theta eq...

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