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Show that cot.(pi)/(20). cot .(3pi)/(2...

Show that
`cot.(pi)/(20). cot .(3pi)/(20). cot.(5pi)/(20). cot .(7pi)/(20). cot.(9pi)/(20)=1`

A

`-1`

B

`1`

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 A ( TRIGONOMETRIC FUNCTIONS)
  1. sin""(3pi)/(5)+ sin""(4pi)/5+sin""(6pi)/(5)+sin""(7pi)/(5)=

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  2. tan 10^(@)*tan20^(@)*tan30^(@)*tan40^(@)*tan50^(@)*tan60^@tan70^(@)*ta...

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  3. Show that cot.(pi)/(20). cot .(3pi)/(20). cot.(5pi)/(20). cot .(7pi)...

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  4. cos 690^(@) * sin 840^(@) + cos 420^(@) * sin 1050^(@)=

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  5. tan 585^(@) * cot 405^(@) + tan 675^(@) * cot 765^(@)=

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  6. sin 420^(@) * cos 390^(@)- cos(-330^(@))* sin(-300^(@))=

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  7. sin 120^(@) cos 150^(@)- cos 240^(@) sin 330^(@) =

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  8. cos^(2)""(pi)/(5)+ sin^(2)""(4pi)/(5)=

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  9. sin^(2)""(2pi)/(3)+ cos^(2)""(5pi)/6-tan^(2)""(3pi)/4=

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  10. cos^(2)1^(@)+ cos^(2)2^(@)+cos^(2)3^(@)+....+cos^(2)90^(@)=

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  11. cos^(2)(80^(@) + theta ) + sin^(2)(100^(@)- theta )=

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  12. sum(k=1)^3 cos^(2)((2k-1)(pi)/(12))=

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  13. tan(45^(@)+ theta )*tan(45^(@)-theta)=

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  14. cos A + sin(270^(@) +A)-sin(270^(@)-A)+ cos(180^(@)-A)=

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  15. "cosec"(270^(@)-A)+"cosec"(90^(@)-A)+sec(90^(@)-A)+sec(270^(@)-A)=

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  16. If "cosec"(pi//2+ theta )+x cos theta cot(pi//2-theta )=sin(pi//2+ the...

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  17. In Delta ABC, cos""((3A+2B+C)/(2))+ cos""((A-C)/(2))=

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  18. In Delta ABC, cos""((B+2C+3A)/(2))+ cos""((A-B)/(2))=

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  19. In DeltaABC , tan""((A+B)/(2))*tan""(C)/(2)=

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  20. If A,B,C,D are the angles of a cyclic quadrilateral then sinA+sinB=

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