Question 1207278
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The given equation is  cos(2x+10) = sin(x+20).


It is assumed that the arguments of sine and cosine are in degrees.
Also, it is assumed, that the solution should be found in the interval 0 <= x < 360 degrees.


Use the identity cos(90-theta) = sin(theta)


Substituting the values we get,

    90-theta = 2x+10      (1)
       theta = x+20       (2)


We have simultaneous equations in two unknowns.
Exclude theta by adding equations 1 and 2

    90-theta+theta = 2x+10+x+20

    90 = 3x+30

    3x+30 = 90

    3x = 90-30 = 60

    x = 20


<U>ANSWER</U>.  x = 20 degrees.
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Solved.