Grade 10Trigonometry
if x=cosA+isinA and √1-c2=nc-1 then prove that 1+ccosA=c/2n(1+nx)(1+n/x)
if x=cosA+isinA and √1-c2=nc-1 then prove that 1+ccosA=c/2n(1+nx)(1+n/x)
1 Answer
Rajat
x= eiA
√(1-c2)=nc-1
or, 1-c2 = (nc)2 +1+2nc
or, c^2(n^2+1) = 2nc
or, c(n^2+1)=2n
or, c = 2n/(n^2+1)
LHS= 1+2n(cosA)/(n^2+1)
RHS= (1+e^iA)(1+e^-iA)/(n^2+1)
= [1+n(e^iA+e^-iA) +n^2]/(n^2+1)
= [1+ n(cosA+isinA+cosA-isinA)+n^2]/(n^2+1)
= [ 1+ 2ncosA+ n^2]/(n^2+1)
= 1 + 2ncosA/(n^2+1)
= LHS
hence proved, pls approved
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