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

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Final answer to the problem

$\frac{\left(\sec\left(a\right)-\tan\left(a\right)\right)\cos\left(a\right)}{\sin\left(a\right)+1}$
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Step-by-step Solution

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

Why is tan(x) = sin(x)/cos(x) ?

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

$\frac{\sec\left(a\right)+\frac{-\sin\left(a\right)}{\cos\left(a\right)}}{\sec\left(a\right)+\frac{\sin\left(a\right)}{\cos\left(a\right)}}$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (sec(a)-tan(a))/(sec(a)+tan(a)). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Combine \sec\left(a\right)+\frac{\sin\left(a\right)}{\cos\left(a\right)} in a single fraction. Applying the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right) = 1. Divide fractions \frac{\sec\left(a\right)+\frac{-\sin\left(a\right)}{\cos\left(a\right)}}{\frac{\sin\left(a\right)+1}{\cos\left(a\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}.

Final answer to the problem

$\frac{\left(\sec\left(a\right)-\tan\left(a\right)\right)\cos\left(a\right)}{\sin\left(a\right)+1}$

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Function Plot

Plotting: $\frac{\left(\sec\left(a\right)-\tan\left(a\right)\right)\cos\left(a\right)}{\sin\left(a\right)+1}$

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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

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