Try NerdPal! Our new app on iOS and Android

# Prove the trigonometric identity $\csc\left(x\right)\tan\left(x\right)=\sec\left(x\right)$

Go!
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:

$\csc\left(x\right)\cdot\tan\left(x\right)=\sec\left(x\right)$

Choose the solving method

1

The tangent function is inverse to the cotangent: $\tan(x)=\frac{1}{\cot(x)}$

$\csc\left(x\right)\frac{1}{\cot\left(x\right)}=\sec\left(x\right)$

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

$\csc\left(x\right)\frac{1}{\cot\left(x\right)}=\sec\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)tan(x)=sec(x). The tangent function is inverse to the cotangent: \tan(x)=\frac{1}{\cot(x)}. Multiply the fraction and term. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Divide fractions \frac{\frac{1}{\sin\left(x\right)}}{\cot\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.

true
$\csc\left(x\right)\cdot\tan\left(x\right)=\sec\left(x\right)$

### Main topic:

Trigonometric Identities

~ 0.05 s