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If A+B+C = 2S, then prove that sin(S-A...

If `A+B+C = 2S`, then prove that
`sin(S-A)+sin(S-B)+sinC = 4 cos ((S-A)/2) cos ((S-B)/2) sin C/2`.

A

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

B

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

C

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

D

`sin A sin B `

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

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

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

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

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

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  9. If A+B+C=(3pi)/(2), prove that cos 2A+ cos 2B+ cos 2C=1-4 sin A sin B ...

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  10. If A+B +C = 270^@, then cos 2A + cos 2B +cos 2C +4sin A sin B sin C=

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

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  12. If A+B+C = 2S, then prove that sin(S-A)+sin(S-B)+sinC = 4 cos ((S-A)...

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  13. If A+B+C= 2S , " then " sin (S-A) sin(S-B) + sinS sin(S-C)=

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  14. If A+B+C = 2S , then P.T cos(S-A)+cos(S-B)+cos(S-C)+cosS=4cos.(A)/(...

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  15. If A+B+C=2S , " then " cos^(2)S + cos^(2)(S-A)+cos^(2)(S-B)+cos^(2)(S-...

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  17. If alpha + beta + gamma = 2 theta , " then " cos theta + cos ( theta...

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

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  19. If A+B+C+D=360^(@), the prove that cos 2A + cos 2B + cos 2C + cos 2D =...

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  20. If A+B+C+D= 2pi , " then " -4 cos""((A+B)/(2)) sin""((A+C)/(2)) cos""(...

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