Grade 11Trigonometry
If a×sin^2 x+ b×cos^2 x =c ,bsin^2y+a cos^2 y=d and a tanx=b tany then prove that a^2/b^2=d-a/b-c ×c-a/b-d
If a×sin^2 x+ b×cos^2 x =c ,bsin^2y+a cos^2 y=d and a tanx=b tany then prove that a^2/b^2=d-a/b-c ×c-a/b-d
1 Answer
sushmitha raj
R.H.S =d-a/b-c=bsin^2y+acos^2y-1/b-asin^2x-bcos^2x
=sin^2y(b-a)/sin^2x(b-a)
sin^2y/sin^2x
similarly,
c-a/b-d=cos^2x/cos^2y
(d-a/b-c)(c-a/b-d)=tan^2y/tan^2x
L.H.S=a^2/b^2
from,atanx=btany
a/b=tany/tanx
a^2/b^2=tan^2y/tan^2x
Hence,proved
REGARDS
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