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If p and q are the solutions of the equation a.tanx + b.secx = c. Then find tan(p+q) = ?

If p and q are the solutions of the equation a.tanx + b.secx = c. Then find tan(p+q) = ?

Grade:11

1 Answers

Aditya Gupta
2081 Points
4 years ago
write eqn as bsecx= c – atanx
square both sides
b^2(1+t^2)= c^2 + a^2*t^2 – 2act, where t= tanx/
or t^2(b^2 – a^2)+2act+b^2 – c^2= 0
clearly, the above eqn has the roots t1= tanp and t2= tanq.
now, sum of roots= tanp+tanq= – 2ac/(b^2 – a^2) and pdt of roots= tanp*tanq= (b^2 – c^2)/(b^2 – a^2)
so you can now easily find tan(p+q)= (tanp + tanq)/(1 – tanp*tanq) in terms of a, b and c by substituting the above derived expressions for tanp + tanq and tanp*tanq.
kindly approve :)

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