Simplify the trigonometric expression $\frac{1+\tan\left(x\right)^2}{\csc\left(x\right)^2}+\sin\left(x\right)^2+\frac{1}{\sec\left(x\right)^2}$

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Final answer to the problem

$\sec\left(x\right)^2$
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Applying the trigonometric identity: $\displaystyle\frac{1}{\sec^{n}(\theta)}=\cos^{n}(\theta)$

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$\frac{1+\tan\left(x\right)^2}{\csc\left(x\right)^2}+\sin\left(x\right)^2+\cos\left(x\right)^2$

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Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (1+tan(x)^2)/(csc(x)^2)+sin(x)^21/(sec(x)^2). Applying the trigonometric identity: \displaystyle\frac{1}{\sec^{n}(\theta)}=\cos^{n}(\theta). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Applying the trigonometric identity: 1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2. Simplify \frac{\sec\left(x\right)^2}{\csc\left(x\right)^2} using trig identities.

Final answer to the problem

$\sec\left(x\right)^2$

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Function Plot

Plotting: $\sec\left(x\right)^2$

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7
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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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