In triangle PQR, ∠R = π/2, if tan P/2 and tan Q/2 are roots of quadratic equation ax²+bx+c=0 where a ≠ 0 then(a) b=c(b) b = a+c(c) a= b+c(d) c = a+b
Rohit Singh , 5 Years ago
Grade 11
1 Answers
Arun
Last Activity: 5 Years ago
ax^2 +bx + c =0 sum of roots tanP/2 + tanQ/2 = -b/a product of roots tanP/2 tanQ/2 = c/a tan (P/2 +Q/2 ) =( tanP/2 + tanQ/2 )/1- tanP/2 tanQ/2 or tan 45 = {-b/a }/ 1- c/a [ P +Q = 90 so P/2 + Q/2 = 45 ] or 1 = -b / (a-c) or a - c = -b or a + b -c =0 Q . E. D.
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