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...
Can't find a method? Tell us so we can add it.
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Your Personal Math Tutor. Powered by AI

Available 24/7, 365 days a year.

Complete step-by-step math solutions. No ads.

Access in depth explanations with descriptive diagrams.

Choose between multiple solving methods.

Download unlimited solutions in PDF format.

Premium access on our iOS and Android apps.

Join 1M+ students worldwide in problem solving.

Choose the plan that suits you best:
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account