Solve the equations |sin x|=|cos x| and `sqrt 3*ctg x = 2*|cos x|`

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The absolute value of a number has the same value irrespective of the sign.

|sin x| = |cos x|

=> sin x = cos x and sin x = -cos x

=> tan x = 1 and tan x = -1

=> x = arc tan 1 and x = arc tan (-1)

=> x = 45 degrees and x = -45 degrees

`sqrt3 *ctg x = 2*|cos x|`

=> `sqrt 3*cos x/sin x = 2*cos x and sqrt 3*cos x/sin x = -2*cos x`

=> `sin x = sqrt 3/2 and sin x= -sqrt 3/2`

=> x = 60 degrees and x = -60 degrees.

The solution of |sin x| = |cos x| is {-45, 45} and that of `sqrt 3*ctg x = 2*|cos x|` is {-60, 60}

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