# prove that sinx+cosx=1

### 2 Answers | Add Yours

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 `

We cannot prove that sin x + cos x = 1 as this is not the case for all values of x.

If we look at the graph of y = sin x + cos x, it is the following:

The values that y takes on lie in the interval `[-sqrt 3, sqrt 3]`

This shows that it is not possible to prove that sin x+cos x=1 as that is not the case.