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In DeltaABC,(sin 2A+ sin 2B+ sin 2C)/(si...

In `DeltaABC,(sin 2A+ sin 2B+ sin 2C)/(sin A + sin B+ sin C)= `

A

`4 sin""(A)/(2) sin""(B)/(2) sin""(C)/(2) `

B

`4 cos""(A)/(2) cos""(B)/(2) cos""(C)/(2)`

C

`8sin""(A)/(2)sin""(B)/(2)""sin""(C)/(2)`

D

`1+4 sin""(A)/(2)sin""(B)/2 sin""(C)/(2)`

Text Solution

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 E ( TRIGONOMETRIC IDENTITIES )
  1. If A+B+C=180^(@) " then " sin A + sin B+ sin C =

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  2. If A+B+C=180^@ " then " sin A + sin B- sin C=

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  3. In DeltaABC,(sin 2A+ sin 2B+ sin 2C)/(sin A + sin B+ sin C)=

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  4. If A+B+C=180^(@) " then " cos A + cos B+ cos C =

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  5. If A+B+C=180^(@) " then " cos A - cos B+ cos C =

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  6. In Delta ABC, (sin 2A + sin 2B+ sin 2C)/(cos A + cos B+ cos C-1)=

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  7. If A, B , C are angles in a triangle, then prove that sin ^(2)A+ sin...

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  8. If A+B+C=180^(@) " then " sin^(2) A - sin^(2)B-sin^(2)C=

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  9. If A+B+C=180^@ " then " cos^(@) A + cos^(2)B + cos^(2)C=

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  10. If A, B, C are angles in a triangle , then prove thatcos^(2)A+cos^(2...

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  11. If A+B+C=180^(@) " then " sin^(2)""(A)/(2)+sin^(2)""(B)/2+sin^(2)""(C)...

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  12. If A+B+C=180^@ " then " sin^(2)""(A)/(2)-sin^(2)""(B)/(2)+sin^(2)""(C)...

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  13. If A+B+ C =pi, then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2...

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

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  15. If A+B+C=180^(@) then prove the following: "cos"A/2+"cos"B/2+"cos"C/...

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  16. If A, B, C are the angles in a triangle then prove that sin .(A)/(2)+...

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  17. If A+B+C=180^@ " then " sin 3A+ sin 3B+ sin 3C=

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  18. If A+B+C=180^(@) " then " cos 3A + cos 3B+ cos 3C=

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  19. If A+B+C=180^@ then sin^(3) A cos (B-C) + sin^(3)B cos(C-A)+ sin^(3) ...

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  20. If A+B+C=180^(@) " then " tan^(2) ""(A)/(2) + tan^(2)""(B)/(2) + tan^(...

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