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find,in terms of pi,all the values of x between 0 and pi which satisfy the equation tan x +cot x =8cos2x

Guest Feb 19, 2017
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tan x +cot x =8cos2x

 

sin(x) / cos (x)   + cos(x) / sin(x)  =  8cos (2x)

 

sin^2(x) + cos^2(x)  / [ sin(x)cos(x)]  =  8cos(2x)

 

1 / [sin(x)cos(x)] = 8cos(2x)

 

1/[ sin(2x)/2 ]   = 8cos(2x)

 

2 / sin(2x)  = 8sos(2x)

 

1/ sin(2x)  = 4cos(2x)

 

1/4  =  cos(2x)sin(2x)

 

1/4  =  (1/2)sin(4x)

 

2/4  =  sin(4x)

 

1/2 = sin(4x)

 

sin (4x)  = 1/2    when  4x = pi/6,   5pi/6,  13pi/6   and  17pi/6  

         

                            so      x = pi/24, 5pi/24, 13pi/24 and  17pi/24

 

 

 

cool cool cool

CPhill  Feb 19, 2017

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