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

Step-by-step explanation

Problem to solve:

$\frac{1}{\cos\left(x\right)}-\frac{\cos\left(x\right)}{1+\sin\left(x\right)}=\tan\left(x\right)$

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

$\frac{1}{\cos\left(x\right)}+\frac{-\cos\left(x\right)}{1+\sin\left(x\right)}=\tan\left(x\right)$

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

true
$\frac{1}{\cos\left(x\right)}-\frac{\cos\left(x\right)}{1+\sin\left(x\right)}=\tan\left(x\right)$

Main topic:

Trigonometric Identities

18

Time to solve it:

~ 0.16 s (SnapXam)