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

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

A

`1-2sin""(A)/(2) sin""(B)/(2) sin""(C)/(2)`

B

`1-2cos""(A)/(2)cos""(B)/(2)cos""(C)/(2)`

C

`1-2cos""(A)/(2)cos""(B)/(2)sin""(C)/(2)`

D

`1-2sin""(A)/(2) cos""(B)/(2) sin""(C)/(2)`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 E ( TRIGONOMETRIC IDENTITIES )
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  2. If A, B, C are angles in a triangle , then prove thatcos^(2)A+cos^(2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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