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If A+B+C=180^(@) then prove the followin...

If `A+B+C=180^(@)` then prove the following:
`"cos"A/2+"cos"B/2+"cos"C/2`
`=4cos((pi-A)/4)cos((pi-B)/4)cos((pi-C)/4)`

A

`cos A + cos B + cos C `

B

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

C

`sin A + sin B + sin C `

D

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

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 E ( TRIGONOMETRIC IDENTITIES )
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  2. In Delta ABC, cos^(2)""(A)/(2)+cos^(2)""(B)/(2)-cos^(2)""(C)/2=

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

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

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

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

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

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

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

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  10. In Delta ABC, if tan ""(A)/(2), tan""(B)/(2) , tan""(C)/(2) are in A.P...

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  11. If A+B+C=pi and cos A = cos B cos C " then " cot B cot C =

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  12. If A+B+C= 90^(@) " then " sin 2A+ sin 2B- sin 2C=

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

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

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  15. If A+B+C=90^(@) " then " cos^(2) A + cos^(2) B + cos^(2) C =

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  16. If A+B+C=90^(@) " then " ( cos 2A + cos 2 B+ cos 2C-1)/( sin A sin B s...

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  17. If A+B+C=0, then prove that sin 2A + sin 2B+ sin 2C=-4sin A sin B sin ...

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  18. If A+B+C=0^@ " then " sin A + sin B + sin C =

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  19. A + B+ C =0అయితే , cos^(2) A + cos^(2) B +cos^(2)C = 1+2 cos A cos B c...

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  20. A + B+ C =0అయితే , cos^(2) A + cos^(2) B +cos^(2)C = 1+2 cos A cos B c...

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