Question 1182143
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Which of the following values of x is a solution to the equation sinx + cos x = 1? 
Think about the graphs of sine and cosine separately.
x=45°
x=90°
x=135°
x=180°
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Starting from

    sin(x) + cos(x) = 1,      (1)


square both sides

    {{{sin^2(x) + 2sin(x)*cos(x) + cos^2(x)}}} = 1.      (2)



Take into account that  {{{sin^2(x)}}} + {{{cos^2(x)}}} == 1.


You will get then from  (2)


    2*sin(x)*cos(x) = 0,

or

      sin(x(*cos(x) = 0.


So, equation (1) implies

    sin(x) = 0  or  cos(x) = 0.


It gives  x = {{{k*pi}}}  or  x = {{{pi/2 + k*pi}}},   where k is any integer number.


Checking these potential solutions,  we get the final answers  x = {{{2pi*n}}},  or  x = {{{pi/2 + 2pi*n}}},  where n is any integer number.


Of the given four optional choices,  only  x= 90°  is the solutions to the given equation.
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Solved.