Asked by kd

Given that. sin 2x = cos (3x - 10), find tanx
2x = 90 -(3x -10)
2x = 90 -3x + 10
2x = -3x + 100
2x + 3x = -3x + 3x + 100
5x = 100
x = 20
tanx = sin/cos
tan = sin40/cos50
Is that correct
Answered by Reiny
your x = 20 if x is in degrees

so tan x = tan20, which is not a rational number.
my calculator says: .36397...

why are you saying tanx = sin40/cos50 ??
tanx = sinx/cosx = sin20/cos20 = .36397...
Answered by Bosnian
Reiny is right to wonder when you wrote:

tan x = sin 40 / cos 50

because

sin( 4​0° ) = cos( 90° − 40° ) = cos 50°

so

sin 40° / cos 50°= cos 50° / cos 50° = 1
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