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Exercise

$sin\left(x\right)-\frac{\sqrt{2}}{2}=0$

Step-by-step Solution

1

To prove that an equation is not an identity, we only need to find one input at which both sides of the equation result in different values

Since we're dealing with trig functions, we can try with different angles as input, such as: $0^{\circ}, 30^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ}...$
2

If we try with the following value

$x=0$
3

After substituting the value and simplify on the left side, we get

$\frac{-\sqrt{2}}{2}$
4

After substituting the value and simplify on the right side, we get

0
5

Since the values of $\sin\left(x\right)+\frac{-\sqrt{2}}{2}$ and $0$ are unequal for $x=0$, we conclude that the equation is not an identity

The equation is not an identity

Final answer to the exercise

The equation is not an identity

Try other ways to solve this exercise

  • Verify if true (using arithmetic)
  • Express in terms of sine and cosine
  • Simplify
  • Simplify into a single function
  • Express in terms of Sine
  • Express in terms of Cosine
  • Express in terms of Tangent
  • Express in terms of Cotangent
  • Express in terms of Secant
  • Express in terms of Cosecant
  • Load more...
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