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Trigonometry Examples
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Trigonometry
Simplify (sin(x+y))/(sin(x)cos(y))
sin
(
x
+
y
)
sin
(
x
)
cos
(
y
)
sin
(
x
+
y
)
sin
(
x
)
cos
(
y
)
Step 1
Separate
fractions
.
1
cos
(
y
)
⋅
sin
(
x
+
y
)
sin
(
x
)
1
cos
(
y
)
⋅
sin
(
x
+
y
)
sin
(
x
)
Step 2
Rewrite
sin
(
x
+
y
)
sin
(
x
)
sin
(
x
+
y
)
sin
(
x
)
as a
product
.
1
cos
(
y
)
(
sin
(
x
+
y
)
1
sin
(
x
)
)
1
cos
(
y
)
(
sin
(
x
+
y
)
1
sin
(
x
)
)
Step 3
Write
sin
(
x
+
y
)
sin
(
x
+
y
)
as a
fraction
with
denominator
1
1
.
1
cos
(
y
)
(
sin
(
x
+
y
)
1
⋅
1
sin
(
x
)
)
1
cos
(
y
)
(
sin
(
x
+
y
)
1
⋅
1
sin
(
x
)
)
Step 4
Simplify.
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Step 4.1
Divide
sin
(
x
+
y
)
sin
(
x
+
y
)
by
1
1
.
1
cos
(
y
)
(
sin
(
x
+
y
)
1
sin
(
x
)
)
1
cos
(
y
)
(
sin
(
x
+
y
)
1
sin
(
x
)
)
Step 4.2
Convert from
1
sin
(
x
)
1
sin
(
x
)
to
csc
(
x
)
csc
(
x
)
.
1
cos
(
y
)
(
sin
(
x
+
y
)
csc
(
x
)
)
1
cos
(
y
)
(
sin
(
x
+
y
)
csc
(
x
)
)
1
cos
(
y
)
(
sin
(
x
+
y
)
csc
(
x
)
)
1
cos
(
y
)
(
sin
(
x
+
y
)
csc
(
x
)
)
Step 5
Convert from
1
cos
(
y
)
1
cos
(
y
)
to
sec
(
y
)
sec
(
y
)
.
sec
(
y
)
sin
(
x
+
y
)
csc
(
x
)
sec
(
y
)
sin
(
x
+
y
)
csc
(
x
)
⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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