SOLUTION: Cosx =Sinx-1

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Question 1174488: Cosx =Sinx-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


cos%28x%29+=+sin%28x%29+-+1.......square both sides
cos%5E2%28x%29+=+%28sin%28x%29+-+1%29%5E2
cos%5E2%28x%29+=+sin%5E2%28x%29+-+2sin%28x%29%2B1
0=+sin%5E2%28x%29+-+2sin%28x%29%2B1-cos%5E2%28x%29+.... use identity 1-cos%5E2%28x%29=sin%5E2%28x%29
0=+sin%5E2%28x%29+-+2sin%28x%29%2Bsin%5E2%28x%29+
0=+2sin%5E2%28x%29+-+2sin%28x%29
0=%28sin%28x%29+-+1%29%2A2sin%28x%29
solutions:
if 0=%28sin%28x%29+-+1%29=>sin%28x%29+=1
if 0=2sin%28x%29=>sin%28x%29+=0
solutions
in radians:
if sin%28x%29+=0
x=2pi%2An
x=pi+%2B2pi%2An+
if sin%28x%29+=1
x=+pi%2F2%2B2pi%2An

in degrees:
x=180°+360°*n
x=90°+360°*n