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

# Prove the trigonometric identity $\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}=\sec\left(x\right)$

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

true

##  Step-by-step Solution 

Problem to solve:

$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}=\sec\left(x\right)$

Specify the solving method

1

Starting from the left-hand side (LHS) of the identity

$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}$

Learn how to solve differential calculus problems step by step online.

$\frac{\sec\left(x\right)-1}{1-\cos\left(x\right)}$

Learn how to solve differential calculus problems step by step online. Prove the trigonometric identity (sec(x)-1)/(1-cos(x))=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Simplify the fraction \frac{\frac{1-\cos\left(x\right)}{\cos\left(x\right)}}{1-\cos\left(x\right)} by 1-\cos\left(x\right).

true

##  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

Prove from RHS (right-hand side)Express everything into Sine and Cosine

### Main topic:

Differential Calculus

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

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