What is the value of x? sin(x+11)°=cos(2x+22)°

answers:     where n is an integer.======the stuff inside the cosine can be factored.    cosine double angle identity can be used, with x+11 as the angle being doubled.we can use the alternate form of the cosine double angle identity that uses sine only, since the other part of the equation involves sine.    hence    if we move all terms to one side, we get    this can be factored and solved like a quadratic.if we let  then    because  find two numbers that multiply to get -2 and add to get 1.these two numbers are 2 and -1    zero factor property: either factor can be equal to zero to satisfy this equation. and remember that a is sin(x+11)for (2a-1), we have    gives the angles that have a sine ratio of 1/2.two angles have a positive sine ratio of 1/2: 30 degrees and 150 degrees (refer to unit circle, etc.)therefore, for 30 degrees:     because co-terminal angles.for 150 degrees, do the same steps to get      for (a+1)    gives the angles with a sine ratio of -1.this is 270 degrees    your answers are    where n is an integer.

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