Grade 11Trigonometry
sin x/a = cos x /b, prove that, a sin 2x + b cos 2x = b
sin x/a = cos x /b, prove that, a sin 2x + b cos 2x = b
2 Answers
Arun
Dear Manoj
tan x = a/b
cos x = b/ (a2+b2)1/2 , , sinx = a/ (a2+b2)1/2
b cos2x + a sin 2x = b (2cos2x-1) + a (2 sin x . cosx)
b( 2 .b2/a2+b2-1) + a ( 2 .a/(a2+b2)1/2.b/(a2+b2)1/2
= b(2b2- a2-b2)/a2+b2 + (2a2b/ a2+b2)
=b (b2-a2)/a2+b2 +2a2b/a2+b2
=b (b2-a2+2a2)/a2+b2
= b = R.H.S.
Regards
Arun
Lalitha Ghanapuram
Answer..
a Sin2x + b cos2x = a ( 2 sinx cosx)+b ( cos²x - sin²x)
[since b sinx=a cosx]
=2 sinx (a cosx)+b cos²x- b sin²x
=2 sinx (b sinx)+b cos²x- b sin²x
=2b sin²x + b cos²x - b sin²x
= b sin²x + b cos²x
= b( sin²x + cos²x)
= b (1)
= b
Hence a Sin2x + b cos2x = b
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