Step-by-step Solution

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

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

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

Learn how to solve trigonometric identities problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sec(x)-1)/(1-cos(x))=sec(x). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine \frac{1}{\cos\left(x\right)}-1 in a single fraction. 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). Applying the trigonometric identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.

Final Answer

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

Related formulas:

1. See formulas

Time to solve it:

~ 0.06 s (SnapXam)