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If A, B, C are angles of a triangle , ...

If `A, B, C ` are angles of a triangle , prove that ` cos 2A - cos 2B + cos 2C =1 -4 sin A cos B sin C `

A

`1-4 sin A sin B sin C `

B

`1- 4 cos A cos B cos C `

C

`1- 4 cos A cos B sin C `

D

`1- 4 sin A cos B sin C `

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 E ( TRIGONOMETRIC IDENTITIES )
  1. If A+B+C= 180^(@) , " then " ( sin 2A- sin 2B- sin 2C)/(sin 2B- sin 2A...

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  2. If A+ B+C= 180^(@) " then " cos 2A+ cos 2B + cos 2C+ 1=

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  3. If A, B, C are angles of a triangle , prove that cos 2A - cos 2B + ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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