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```				   in a triangle abc if the product of sines of the angles of a triangle is P and if the product of cosines of a triangle is Q then the equation whose roots are tanA,tanB,tanC is?

```

7 years ago

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```										Dear sameer sai
given
sinA sinB sinC=p
cosA cosB cosC =q
so tanA tanB tanC =p/q
and A+B+C=180
use tan(a+b+c) formula
u will get  tanA+tanB+tanC=tanA tanB tanC
so        tanA+tanB+tanC=p/q
now
tanAtanB +tanB tanC+ tanC tanA=(sinA sinB cosC +sinB sinC cosA +sinC sinA cosB)/cosA cosB cosC
=1/q (sinA sinB cosC +sinC [sinB cosA + sinA cosB])
=1/q (sinA sinB cosC +sinC [sin(A+B)])
=1/q (sinA sinB cosC +sin2C )
=1/q (sinA sinB cosC +1-cos2C )
=1/q (1+cosC{-cosC+sinA sinB } )
=1/q (1+cosC cosA cosB  )
=1/q (1+q )
now  u can get equation.
qx3 -px2 +(1+q)x -p =0

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.  All the best.  Regards, Askiitians Experts Badiuddin

```
7 years ago

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