IF 3sinA + 5cosA = 5 PROVE THAT: 5sinA - 3cosA = plus or minus 3 and HENCE FIND (3 - 5tanA)/(5 + 3tanA)

Asked by  | 25th Sep, 2010, 01:30: PM

Expert Answer:

Dear Student,
 
Given equation is
 
3sinA + 5cosA = 5
 
=> 3sinA = 5(1 - cosA)
 
=> 9sin2A = 25(1 + cos2A - 2cosA)
 
=> 9(1-cos2A) = 25 + 25cos2A - 50cosA
 
=> 34cos2A - 50cosA + 8 = 0
 
solving the quadratic equation, we get
 
cosA = 1 or cosA = 8/17
 
=> sinA = 0 or sinA = 15/17
 
 
Hence, when cosA = 1, we have
 
5sinA - 3cosA = 5 x 0 - 3 x 1 = -3
 
and when cosA = 8/17, we have
 
5 x 15/17 - 3 x 8/17 = (75 - 24)/17 = 51/17 = 3
 
Therefore, 5sinA - 3cosA = 3 or -3.
 
Regards Topperlearning.

Answered by  | 26th Sep, 2010, 01:02: PM

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