SOLUTION: Please help me with the problem below: Solve the equation and find all real solutions: (sinx +cosx)^2 = 1

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me with the problem below: Solve the equation and find all real solutions: (sinx +cosx)^2 = 1      Log On


   

Question 1000865: Please help me with the problem below:
Solve the equation and find all real solutions:
(sinx +cosx)^2 = 1
Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve the equation and find all real solutions:
(sinx +cosx)^2 = 1.
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Open parentheses and then simplify

sin%5E2%28x%29+%2B+2%2Asin%28x%29%2Acos%28x%29+%2B+sin%5E2%28x%29 = 1,

1 + 2*sin(x)*cos(x) = 1,       <------ sin%5E2%28x%29+%2B+cos%5E2%28x%29 = 1

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

sin(2x) = 0,                         (formula of the double argument for sine)

2x = k%2Api,   k = 0, +/- 1, +/- 2, . . . (integers)

x = %28k%2Api%29%2F2.