ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

Prove the trigonometric identity $\frac{\csc\left(x\right)}{\cot\left(x\right)}=\sec\left(x\right)$

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 

Specify the solving method

1

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

$\frac{\csc\left(x\right)}{\cot\left(x\right)}$
2

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

$\frac{\frac{1}{\sin\left(x\right)}}{\cot\left(x\right)}$

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

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)/cot(x)=sec(x). Starting from the left-hand side (LHS) of the identity. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Simplify the fraction \frac{\frac{1}{\sin\left(x\right)}}{\frac{\cos\left(x\right)}{\sin\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: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.