general solution  cos (4x-60)=sin2x [-90:90]  

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Solve `cos(4x-60^@)=sin2x ` :

`cos(4x-60^@)=sin2x `

`sin(4x+30^@)=sin2x `

Take the inverse sine of both sides:

1. `4x+30=180-2x+360n ` where n is an integer.

6x=150+360n

x=25+60n

or

2. 4x+30=2x+360n

2x=-30+360n

x=-15+180n

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The general solution is x=25+60n for n an integer or x=-15+180n for n an integer.

On the interval [-90,90] the solutions are x=-35,-15,25,85

Here is the graph: the left side in black and the right side in red:

convert the scale from radian to degrees.
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