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

# Prove the trigonometric identity $\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)=\frac{1}{\sec\left(x\right)}$

Go!
Symbolic 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 

How should I solve this problem?

• Prove from LHS (left-hand side)
• Prove from RHS (right-hand side)
• Express everything into Sine and Cosine
• Exact Differential Equation
• Linear Differential Equation
• Separable Differential Equation
• Homogeneous Differential Equation
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
Can't find a method? Tell us so we can add it.
1

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

$\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)$

Learn how to solve problems step by step online.

$\sec\left(x\right)-\tan\left(x\right)\sin\left(x\right)$

Learn how to solve problems step by step online. Prove the trigonometric identity sec(x)-tan(x)sin(x)=1/sec(x). Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiplying the fraction by \sin\left(x\right). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\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