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Prove that (1+cos""pi/10)(1+cos""(3pi)/1...

Prove that `(1+cos""pi/10)(1+cos""(3pi)/10)(1+cos""(7pi)/10)(1+cos""(9pi)/10)=1/16`

A

`1//2`

B

`1//4`

C

`1//8`

D

`1//16`

Text Solution

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 C ( MULTIPLE AND SUBMULTIPLE ANGLES )
  1. cos^(2) A + cos^(2) ( 120^(@) + A)+ cos^(2) (120^(@) - A )=

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  2. cos^(3) theta + cos^(3) ( 120^(@) +theta ) + cos^(3) (120^(@) - theta ...

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  3. sin^(2) 20^(@) + sin^(2) 100^@ + sin^(2) 140^(@) =

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  4. cos^(3) 20^(@) + cos^(3) 100^(@) + cos^(3) 140^(@) =

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  5. cos^(2)(theta-45^(@))+cos^(2)(theta+15^(@)-cos^(2)(theta-15^(@))=

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  6. If 4 sin(60^(@) + theta ) sin (60^(@) - theta )-1=k cos 2 theta , th...

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  7. Show that sin ^(4). (pi)/(8)+ sin ^(4) .(3pi)/(8) sin ^(4). (5pi)/(8)...

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  8. Show that cos^4""pi/8+cos^4""(3pi)/8+cos^4""(5pi)/8+cos^4""(7pi)/8=3/2

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  9. tan ""7(1^@)/(2)=

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  10. tan 82(1^(@))/(2)=

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  11. If sin 18^(@)=(sqrt(5)-1)/(4) , then sin 81^(@)=

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  12. Prove that (1)/(cos 290^(@))+(1)/(sqrt3 sin 250^(@) )=(4)/(sqrt3)

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  13. Show that 1/(sin 10^(@)) - (sqrt(3))/(cos 10^(@)) = 4.

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  14. Prove that sqrt3 csc 20 ^(@)- sec 20^(@)=4

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  15. A quadratic equation whose roots are sin^(2) 18^(@) , cos^(2) 36^(@) ...

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  16. Prove that (1+cos""pi/10)(1+cos""(3pi)/10)(1+cos""(7pi)/10)(1+cos""(9p...

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  17. If x+y+z =xyz, then sum(2x)/(1-x^(2))=

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  18. If x+y+z=xyz , " then " sum(3x-x^(3))/(1-3x^(2))=

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  19. If xy+yz+zx=1 , then sum(x+y)/(1-xy)=

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  20. If xy+yz+zx=1 , then sum(2x-)/(1-x^(2))=

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