In a triangle PQR,∠R=π2, if tan(P2) and tan(Q2)𝑃𝑄𝑅,∠𝑅=𝜋2, if tan(𝑃2) and tan(𝑄2) are the roots of the equation ax2+bx+c=0(a≠0)𝑎𝑥2+𝑏𝑥+𝑐=0(𝑎≠0) then
Question
In a triangle PQR, ∠R=π/2, if tan(P/2) and tan(Q/2) are the roots of the equation
then
Solution
The question seems to be incomplete. However, I can provide a general approach to solve such problems.
Given that ∠R = π/2, we know that ∠P + ∠Q = π/2 (since the sum of angles in a triangle is π).
Also, given that tan(P/2) and tan(Q/2) are the roots of the equation ax^2 + bx + c = 0, we can use the properties of roots of quadratic equations.
The sum of the roots of the equation ax^2 + bx + c = 0 is -b/a and the product of the roots is c/a.
Therefore, we have:
tan(P/2) + tan(Q/2) = -b/a tan(P/2) * tan(Q/2) = c/a
We can use these equations along with the given information to solve for the unknowns. However, without the complete question, it's not possible to provide a specific solution.
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