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If the equation a*sin x -2*sin 3 x=2*a -8 has solution, then show that 2≤a≤6

If the equation a*sin x -2*sin3 x=2*a -8 has solution, then show that 2≤a≤6

Grade:10

1 Answers

Vikas TU
14149 Points
7 years ago
The Range of sinx is [-1,1]
 .i.e
 -1
 -1 3x
 
Check conditions on boundary,
for minimum of sinx
the eqn. becomes,
when sin x= -1
=> -a +  2 = 2a – 8
=> 10 = 3a
a = 10/3 = 3.33 (approx)
 
when sinx = 1
 
eqn. becomes,
a -2 = 2a – 8
a = -2 + 8
a = 6
 
therfore range of a is,
  3.33

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