SOLUTION: please help me with the question: sin x=1 - cos x

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Question 998480: please help me with the question: sin x=1 - cos x
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
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please help me with the question: sin x=1 - cos x
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Hey,  this is not a question.  It is an equation.
If you want to solve it,  say  "Please help me solve this equation".

OK,  let's solve it.

sin(x) = 1 - cos(x).

In the left side,  replace  sin(x) = sqrt%281-cos%5E2%28x%29%29 to get the equation for one uniform unknown  cos(x):

sqrt%281-cos%5E2%28x%29%29 = 1+-+cos%28x%29,   ---> square both sides --->

1+-+cos%5E2%28x%29 = 1+-+2%2Acos%28x%29+%2B+cos%5E2%28x%29,

2%2Acos%5E2%28x%29+-+2%2Acos%28x%29 = 0,

2%2Acos%28x%29.%28cos%28x%29-1%29 = 0,

a)  cos(x) = 0   ----->  x = pi%2F2+%2B+k%2Api,  k = 0, +/-1, +/-2, . . .

b)  cos(x) = 1 ----->   x = k%2Api,  k = 0, +/-1, +/-2, . . .