Step-by-step Solution

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

true

Step-by-step Solution

Problem to solve:

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

Solving method

1

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

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

Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$

$\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}=\csc\left(x\right)$
3

Simplify the fraction $\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}$ by $\cos\left(x\right)$

$\frac{1}{\sin\left(x\right)}=\csc\left(x\right)$
4

The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$

$\csc\left(x\right)=\csc\left(x\right)$
5

Since both sides of the equality are equal, we have proven the identity

true

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

Main topic:

Trigonometric Identities

~ 0.03 s