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If x cos alpha = y cos ( 2pi//3+ alpha )...

If `x cos alpha = y cos ( 2pi//3+ alpha ) = z cos ( 4pi//3+ alpha ) , " then " xy+yz+zx=`

A

0

B

1

C

`-1`

D

`2`

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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 C ( MULTIPLE AND SUBMULTIPLE ANGLES )
  1. If 0 lt theta lt pi//4 , " then " sqrt(2+sqrt(2+2cos 4 theta ))=

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  2. If 0 lt x lt pi , and cos x+ sin x =1//2, then tan x=

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  3. If x cos alpha = y cos ( 2pi//3+ alpha ) = z cos ( 4pi//3+ alpha ) , "...

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  4. If (x)/(tan( theta + alpha ))=(y)/(tan (theta + beta ))=(z)/(tan ( the...

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  5. If (x)/( cos theta ) = (y) /( cos (theta - 2pi//3))=(z)/( cos ( theta ...

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  6. If log2(sinx)-log2(cos x)-log2(1-tan x)-log2(1+ tan x)=-1 then tan 2...

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  7. tan x+ tan(x+(pi)/(3))+ tan(x+(2pi)/(3))=3impliestan 3 x=

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  8. If tan theta + tan ( theta + (pi)/(3))+ tan ( theta + (2pi)/(3))=3 , ...

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  9. If tan 35^(@) = k , then the value of ( tan 145^(@) - tan 125^(@))/...

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  10. If "cosec" theta = (p+q)/(p-q) " then " cot((pi)/4+( theta )/(2))=

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  11. If sec ( theta - alpha ) , sec theta , sec ( theta + alpha ) are in ...

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  12. If A=340^(@) " then " sqrt(1- sin A)-sqrt(1+ sin A)=

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  13. If tan^(2) A= 2 tan ^(2) B+1, then 2 cos 2A + 1=

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  14. If tan^(2) A= 2 tan ^(2) B+1, "then " cos 2A + sin^(2)B =

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  15. If 2 tan A=3 tan B , " then " tan (A-B)=

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  16. If tan A = 1//2 , tan B=1//3 " then " cos 2A=

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  17. If cos alpha = (3)/(5) , cos beta =(5)/(13) , "then " cos^(2) ((alpha...

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  18. cos""(2pi)/(15) cos ""(4pi)/(15)""cos(8pi)/(15) cos""(16pi)/(15)=

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  19. Prove that cos. (pi)/(11). cos . (2 pi)/(11). cos . (3 pi)/(11) cos. (...

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  20. cos 10^(@) cos 30^(@) cos 50^(@) cos 70^(@) =

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