👉 Try now NerdPal! Our new math app on iOS and Android

# Prove that $\sin\left(x\right)- \frac{\sqrt{2}}{2}=0$ is not an identity

## Step-by-step Solution

Go!
Math 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

###  Videos

The equation is not an identity

##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

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

$x=0$

Replace the variable $x$ with the value $0$

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

Divide $-\sqrt{2}$ by $2$

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

The sine of $0$ equals $0$

$-\frac{\sqrt{2}}{2}$
3

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

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

Replace the variable $x$ with the value $0$

0
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

The equation is not an identity

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Verify if true (using algebra)

### Main topic:

Differential Calculus

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account