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Trignometry

New kid on the Block

 Joined: 13 Feb 2011 Post: 21
21 Jun 2012 14:55:20 IST
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In a right angled triangle PQR,
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

In a right angled triangle PQR, R = 90 degree. If tan(P/2) and tan(Q/2) are the roots of the equation ax2 + bx + c, give the relation between a, b and c.

Blazing goIITian

Joined: 1 Apr 2007
Posts: 4025
21 Jun 2012 20:24:29 IST
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we know:---

p+q=90

and

tan(P/2) +tan(Q/2) = -b/a

and
tan(P/2).tan(Q/2) = c/a

putting these values in the formula

tan(P/2+Q/2)  = ( tan(P/2)+ tan(Q/2) )/ 1-tan(P/2).tan(Q/2)

we get tan45 = 1

and on further solving we get

a+b=c
all the best

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