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Solve the trigonometric integral $\int\left(\frac{\sin\left(t\right)}{\cos\left(t\right)}\right)^2dt$

Step-by-step Solution

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ln
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sin
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tan
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asin
acos
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sinh
cosh
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asinh
acosh
atanh
acoth
asech
acsch

Final Answer

$\tan\left(t\right)-t+C_0$
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Step-by-step Solution

Problem to solve:

$\int\frac{\sin\left(t\right)}{\cos\left(t\right)}^2dt$

Specify the solving method

1

Simplify $\tan\left(t\right)^2$ by applying trigonometric identities

$\int\tan\left(t\right)^2dt$

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

$\int\tan\left(t\right)^2dt$

Unlock the first 2 steps of this solution!

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(((sin(t)/(cos(t))^2)dt. Simplify \tan\left(t\right)^2 by applying trigonometric identities. Applying the trigonometric identity: \tan^2(\theta)=\sec(\theta)^2-1. Expand the integral \int\left(\sec\left(t\right)^2-1\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sec\left(t\right)^2dt results in: \tan\left(t\right).

Final Answer

$\tan\left(t\right)-t+C_0$
SnapXam A2
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Got another 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

Useful tips on how to improve your answer:

$\int\frac{\sin\left(t\right)}{\cos\left(t\right)}^2dt$

Used formulas:

3. See formulas

Time to solve it:

~ 0.09 s