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In triangle ABC , prove that sin .(A)/(2...

In triangle ABC , prove that `sin .(A)/(2)+ sin. (B)/(2) -sin. (C)/(2)=-1+4 cos.(pi-A)/(4)cos. (pi-B)/(4)sin. (pi-C)/(4)`

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If A+B+C=180^(@) then prove that sin"A/2+"sin"B/2+"sin"C/2 =1+4sin((pi-A)/4)sin((pi-B)/4)cos((pi-C)/4)

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AAKASH SERIES-TRANSFORMATIONS AND INDENTITIES-PRACTIVE EXERCISE
  1. In triangle ABC , prove that sin .(A)/(2)+ sin. (B)/(2) -sin. (C)/(2)=...

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  2. cos70^(@)+sin40^(@)=

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  3. cos(36^(@)-A)cos(36^(@)+A)+cos(54^(@)+A)cos(54^(@)-A)=

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  4. 2(1-2sin^(2)7theta)sin 3 theta=

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  5. (cos 8 A cos 5A-cos 12 A cos 9A)/(sin 8 A cos 5 A +cos 12Asin 9A)=

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  6. ( sin 3 theta + sin 5 theta + sin 7 theta + sin 9 theta)/( cos 3 thet...

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  7. The value of (2 (sin2 theta-2 cos^(2)theta-1))/(cos theta-sin theta-co...

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  8. The value (cos (A+B+C)+cos (A-B-C))/(2 cos (B+C))

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  9. ((cosA+cos B)/(sinA-sinB))^(2013)+((sin A+sin B)/( cos A-cos B))^(2013...

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  10. sin10^(@)+sin20^(@)+sin40^(@)+sin50^(@)-sin70^(@)-sin80^(@)=

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  11. sin 12^(@)sin 48^(@)sin 54^(@)=

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  12. 1+ cos 2x + cos 4 x+ cos 6x- 4 cos x cos 2x cos 3x =

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  13. ( cos 6 x + 6 cos 4 x+ 15 cos 2 x+ 10)/( cos 5 x+ 5 cos 3 x + 10 cos ...

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  14. The value of cos 20^(@)+2sin^(2)55^(@)-1-sqrt(2)sin65^(@)=

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

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  16. If x+y+z=180^(@) then (sinx+siny+sinz)/("cos"x/2."cos"y/2."cos"z/2)=

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  17. If alpha=(pi)/21 then (sin 3 alpha+sin 7 alpha)/(sin 24 alpha+sin 14 a...

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  18. If (sin A-sinC)/(cosC-cosA)=cotB then angles A,B,C are in

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  19. sinx+siny=3/4 andsinx-siny=2/5 then (tan((x-y)/2))/(tan((x+y)/2))=

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  20. tan theta tan (theta+60^(@))+tan theta tan (theta-60^(@))+tan (theta+6...

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  21. cos(x-y)=3cos(x+y) then cotxcoty=

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