Trigonometry
Please tell above answer quickly and as soon as possible with proper explanation
Please tell above answer quickly and as soon as possible with proper explanation
1 Answer
Aditya Gupta
acosx+bsinx=c
now we know the formulas: cosx = (1-t^2)/(1+t^2) and sinx= 2t/(1+t^2) where t = tan(x/2)
so it becomes a(1-t^2)+2bt= c(1+t^2)
or (a+c)t^2 – 2bt+c – a=0
the above equation is a quadratic in t with roots tan(alpha/2) and tan(beta/2).
now tan(alpha+beta)/2= tan(alpha/2+beta/2)= (t1+t2)/(1 – t1t2) where t1 and t2 are tan(alpha/2) and tan(beta/2).
but t1+t2 is the sum of roots= 2b/(a+c) and 1 – t1t2= 1 – product= 1 – (c – a)/(c+a)
so that (t1+t2)/(1 – t1t2) = 2b/(c+a – (c-a))
= 2b/2a
=b/a
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