prove that

sinx+cosx=1

Expert Answers

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sin x + cos x is not equal to 1 for all values of x. This is not a trigonometric identity.

The equation holds for some values of x.

sin x + cos x = 1

=> (sin x + cos x)^2 = 1

=> sin^2x + cos^2x + 2*sin x*cos x = 1

=> 2*sin x*cos x = 0

=> sin 2x = 0

=> `2x = sin^-1 0`

=> x = 0, x = `pi/2 `

The solution of the equation sin x + cos x = 1 is `x = n*2*pi ` and `x = pi/2 + 2*n*pi `

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