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In a DeltaA B C , if (c+a+b)(a+b-c)=a b...

In a ` DeltaA B C` , if `(c+a+b)(a+b-c)=a b` , then the measure of angel `C` is `pi/3` (b)`pi/6` (c) `(2pi)/3` (d) `pi/2`

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GIven,In traingle ABC,`(c+a+b)(a+b-c)=a b`
=`ac + bc – c^2 + a^2 + ab - ac + ab + b^2 - bc - ab = 0 `
=`– c^2 + a^2 + ab + b^2 = 0 `
=`a^2 + b^2 – c^2 = - ab ...(i)`
By Cosine law,
`cos C=(a^2+b^2-c^2)/(2ab)`
`cos C=(-ab)/(2ab)[by (i)]`
`cos C=(-1)/(2)`
...
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. In any DeltaA B C ,2(bc cosA+ ca cosB+ab cosC) =

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  2. In any Delta A B C , the value of 2a csin((A-B+C)/2) is (a)a^2+b^2-c^...

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  3. In a DeltaA B C , if (c+a+b)(a+b-c)=a b , then the measure of angel C...

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  4. If any triangle A B C , that: (b^2-c^2)/(cosB+cosC)+(c^2-a^2)/(cosC+co...

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  5. In a right angled triangle ABC, write the value of sin^2 A + sin^2 B+ ...

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  6. If any triangle A B C , that: (asin(B-C))/(b^2-c^2)=(bsin(C-A))/(c^2-...

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  7. In a Delta A B C , if cosC=(sinA)/(2sinB) , prove that the triangle is...

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  9. (sqrt(sinA)-sqrt(sinB))/(sqrt(sinA)+sqrt(sinB)) = (a+b-2sqrt(ab))/(a-b...

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  10. The angle of elevation of the top of a tower from a point A due south ...

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  11. (bsecB+csecC)/(tanB+t a n C)=(csecC+asecA)/(tanC+t a n A)=(asecA+bsecB...

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  12. a(cosC-cosB)=2(b-c)cos^2A/2

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  13. a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .

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  14. cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2

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  15. In a Delta A B C ,\ if\ a=2,\ b=3\ a n d\ sin A=2/3 then find /B

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  16. In any triangle A B C , prove that: (sin(B-C))/(sin(B+C))=(b^2-c^2)/(a...

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  17. In any triangle A B C , prove that: \ asin(B-C)+b s in(C-A)+csin(A-B)=...

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  18. In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A...

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  19. In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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  20. In any triangle A B C , prove that: (b-c)/(b+c)=(tan((B-C)/2))/(tan((B...

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