Question
Mon April 19, 2010 By:

If x and y are two different values of  lying between 0 and 2pie which satisfy the equation 6cos

Dear sir , please solve this question

Expert Reply
Fri April 23, 2010

Dear Student,

The solution to your problem is as follows:

6cosα + 8sinα = 9

=> (6cosα)2 = (9 - 8sinα )2

=> 36cos2α = 81 + 64sin2α - 144sinα

=>36(1-sin2α) = 81 + 64sin2α - 144sinα

=> 81 - 36 + 64sin2α + 36sin2α - 144sinα = 0

=> 100sin2α - 144sinα + 45 = 0

This is a quadratic eqn in sinα, solving it by D-method, we get the two solutions as

=> sinα = 0.9815 ,  0.4585

=> x = 78.962 , y = 27.288

Hence,

sin(x+y) = sin (78.962 + 27.288) = sin (106.25) = 0.96005

 

Regards Topperlearning.

 

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