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# Solve the trigonometric integral $\int\left(\frac{\sin\left(y\right)}{\cos\left(y\right)}\right)^2dy$

## Step-by-step Solution

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$\tan\left(y\right)-y+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\left(\frac{\sin\left(y\right)}{\cos\left(y\right)}\right)^2dy$

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Simplify $\left(\frac{\sin\left(y\right)}{\cos\left(y\right)}\right)^2$ into $\tan\left(y\right)^2$ by applying trigonometric identities

$\int\tan\left(y\right)^2dy$

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

$\int\tan\left(y\right)^2dy$

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

$\tan\left(y\right)-y+C_0$

##  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

Solve int(((sin(y)/(cos(y))^2)dy using basic integralsSolve int(((sin(y)/(cos(y))^2)dy using u-substitutionSolve int(((sin(y)/(cos(y))^2)dy using integration by partsSolve int(((sin(y)/(cos(y))^2)dy using weierstrass substitution

SnapXam A2

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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

### Main topic:

Trigonometric Integrals

~ 0.07 s

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