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In any A B C , prove that: Delta=(a^2-...

In any ` A B C ,` prove that: `Delta=(a^2-b^2)/2dot(sinAsinB)/(sin(A-B))`

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Given, R.H.S=`(a^2-b^2)/2dot(sinAsinB)/(sin(A-B))`
By sine law,
`a=k sinA,b=k sin B,c=k sin C`
so the equation becomes,
`(k^2.sin^2A-k^2.sin^2B)/2dot(sinAsinB)/(sin(A-B))`
=`([sin(A+B)sin(A-B))/2]((ksinA ksinB)/sin(A-B))`
=`1/2`absin`(A+B)`[by sine law]
=`1/2.a.bsin(180-C)`
...
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
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  2. In a Delta A B C , ifsinAa n dsinB are the roots of the equation c^2...

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  3. In any A B C , prove that: Delta=(a^2-b^2)/2dot(sinAsinB)/(sin(A-B))

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  4. In any triangle A B C , prove that:Delta=(b^2+c^2-a^2)/(4cota) .

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  5. In a triangle A B C ,a=4,b=3,/A=60^@ then c is root of the equation c^...

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  6. In any DeltaA B C ,2(bc cosA+ ca cosB+ab cosC) =

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

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

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  13. Problem on sine rule Type:-2 (i)The angle of elevation of the top of ...

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

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

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

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

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

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

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  20. 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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