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If sin x +7 cos x=5 then tan(x/2) is a root of equation

If sin x +7 cos x=5 then tan(x/2) is a root of equation

Grade:11

1 Answers

RISHIKESH VERMA
26 Points
6 years ago
we know formula   sinx=2*tan(x)/2/(1+tan^x/2)    and cosx=( 1-tan^(x/2))/(1+tan^2(x/2))
let’s assume that tanx/2=p
put this value in given equation
2p/(1+p^2) + 7(1-p^2)/(1+p^2) =5
after solving we get 
6p^2 -p -1=0
2p-1=0    and 3p+1=0
p=1/2     and p=-1/3
tan(x)/2=1/2    and tan(x)/2= -1/3

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