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In a Delta A B C , ifsinAa n dsinB are...

In a `Delta A B C` , if`sinAa n dsinB` are the roots of the equation `c^2x^2-c(a+b)x+a b=0,` then find `/_Cdot`

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According to the product of the roots
`sinAxxsinB=(ab)/(c^2)`
By sine law we get
`sinA=(axxsinC)/c`
and `sin B=(bxxsinC)/c`
So,`sin AxxsinB=[(axxsinC)/c]xx[(bxxsinC)/c]`
`=>(ab)/(c^2)=(ab(sinC)^2)/(c^2)`
`=>1=(sinC)^2`
...
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RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
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  11. In a right angled triangle ABC, write the value of sin^2 A + sin^2 B+ ...

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

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

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

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