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3 Answers
- ?Lv 57 years ago
i am taking theta = t
LET
a=Acosx
b=Asinx
A^2 ( cos^2 x-sin^2 x) sint + Acosx Asinx cost + Acosx Asinx cost = A^2 cos^2 x+ A^2 sin^2 x
cos^2 x sint - sin^2 x sint + cosx sinx cost + cosx sinx cost = 1
cos^2 x sint + cosx sinx cost + cosx sinx cost - sin^2 x sint = 1
cosx( cosx sint + sinx cost ) + sinx ( cosx cost - sinx sint ) = 1
cosx sin(x+t) + sinx cos(x+t) = 1
sin ( x+ x+ t) = 1
sin(2x+t)=1
2x+t = pi/2
t=pi/2 - 2x
taking tan on both sides..
tan t = tan(pi/2 - 2x)
tan t = 1/tan2x
from
a=Acosx
b=Asinx
tanx=b/a
tan2x=2tanx/1-tan^2x
tan2x= 2(b/a)a^2 / (a^2-b^2) = 2ab/(a^2-b^2)
sub back
tan t = 1/tan2x
tant = (a^2-b^2)/2ab
- Anonymous7 years ago
yes
