Try NerdPal! Our new app on iOS and Android

Prove the trigonometric identity $\tan\left(x\right)\cos\left(x\right)\csc\left(x\right)=1$

Step-by-step Solution

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

Final Answer

true

Step-by-step Solution

Problem to solve:

$\tan\left(x\right)\cdot \cos\left(x\right)\cdot \csc\left(x\right)=1$

Specify the solving method

1

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\sin\left(x\right)}{\cos\left(x\right)}\cos\left(x\right)\csc\left(x\right)=1$

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

$\frac{\sin\left(x\right)}{\cos\left(x\right)}\cos\left(x\right)\csc\left(x\right)=1$

Unlock the first 2 steps of this solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)cos(x)csc(x)=1. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiplying the fraction by \cos\left(x\right)\csc\left(x\right). Simplify the fraction \frac{\sin\left(x\right)\cos\left(x\right)\csc\left(x\right)}{\cos\left(x\right)} by \cos\left(x\right). Applying the trigonometric identity: \sin\left(\theta\right)\cdot\csc\left(\theta\right)=1.

Final Answer

true
$\tan\left(x\right)\cdot \cos\left(x\right)\cdot \csc\left(x\right)=1$

Used formulas:

2. See formulas

Time to solve it:

~ 0.03 s