👉 Try now NerdPal! Our new math app on iOS and Android

Simplify the trigonometric expression $\frac{\tan\left(x\right)+\cot\left(x\right)}{\sec\left(x\right)}$

Step-by-step Solution

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

Final Answer

$\frac{\sqrt{1+\tan\left(x\right)^2}}{\tan\left(x\right)}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Expand the fraction $\frac{\tan\left(x\right)+\cot\left(x\right)}{\sec\left(x\right)}$ into $2$ simpler fractions with common denominator $\sec\left(x\right)$

$\frac{\tan\left(x\right)}{\sec\left(x\right)}+\frac{\cot\left(x\right)}{\sec\left(x\right)}$

Learn how to solve simplify trigonometric expressions problems step by step online.

$\frac{\tan\left(x\right)}{\sec\left(x\right)}+\frac{\cot\left(x\right)}{\sec\left(x\right)}$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (tan(x)+cot(x))/sec(x). Expand the fraction \frac{\tan\left(x\right)+\cot\left(x\right)}{\sec\left(x\right)} into 2 simpler fractions with common denominator \sec\left(x\right). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Divide fractions \frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\sec\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}. Applying the trigonometric identity: \sin\left(\theta \right)\sec\left(\theta \right) = \tan\left(\theta \right).

Final Answer

$\frac{\sqrt{1+\tan\left(x\right)^2}}{\tan\left(x\right)}$

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

Express in terms of sine and cosineSimplifySimplify into a single functionExpress in terms of SineExpress in terms of CosineExpress in terms of CotangentExpress in terms of SecantExpress in terms of CosecantFactorFind the derivativeSolve (tanx+cotx)/secx using basic integrals

Give us your feedback!

Function Plot

Plotting: $\frac{\sqrt{1+\tan\left(x\right)^2}}{\tan\left(x\right)}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

Used Formulas

5. See formulas

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account