+0  
 
0
187
1
avatar

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
 #1
avatar+87293 
0

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

17 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.