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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

Grade:11

2 Answers

Arun
25750 Points
5 years ago
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
27 Points
2 years ago
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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