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Prove:cos(pi/15)cos((2pi)/15)cos((3pi)/1...

Prove:`cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)cos((6pi)/15)cos((7pi)/15)` = `1/2^7`

A

`(1)/(2^(6))`

B

`(1)/(2^(7))`

C

`(1)/(2^(8))`

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise
  1. Find the angle theta whose cosine is equal to its tangent.

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  2. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15...

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  3. Prove:cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)co...

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  4. The value of tan 5 theta is

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  5. If costheta=cos alphacosbeta, then tan((theta+alpha)/(2))tan((theta-al...

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  6. If abs(cos theta{sin theta+sqrt(sin^2theta+sin^2alpha)})lek, then the ...

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  7. The value of sin10^@+sin20^@+sin30^@...+sin360^@ is equal to -

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  8. Find the value of the expression 3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(...

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  9. If A+B=(pi)/(4),then (tanA+1)(tanB+1) is equal to

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  10. If sinA+sinB=a and cosA+cosB=b,then cos(A+B)

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  11. If an angle theta is divided into two parts A and B such that A-B=x an...

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  12. The value of the expression is

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  13. If tan((theta)/(2))=5/2and tan((phi)/(2))=3/4, the value of cos(theta+...

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  14. If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gam...

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  15. If sin x+siny=3(cosy-cosx),then the value of (sin3x)/(sin3y), is

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  16. If cosx=tany ,cosy=tanz ,cosz=tanx , then the value of sinx is 2cos18^...

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  17. If k=sin^(6)x+cos^(6)x, then k belongs to the interval

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  18. The value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to

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  19. If tan^(2)alpha tan^(2)beta+tan^(2)gamma+tan^(2)gamma tan^(2)alpha+2ta...

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  20. the value of e^(log(10)tan1^@+log(10)tan2^@+log(10)tan3^@....+log(10)t...

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