simplify sec theta - (tan theta) (sin theta)
Answers
Answer:
sec
(
θ
)
tan
(
θ
)
sin
(
θ
)
Separate fractions.
tan
(
θ
)
1
⋅
sec
(
θ
)
sin
(
θ
)
Rewrite
sec
(
θ
)
in terms of sines and cosines.
tan
(
θ
)
1
⋅
1
cos
(
θ
)
sin
(
θ
)
Rewrite
1
cos
(
θ
)
sin
(
θ
)
as a product.
tan
(
θ
)
1
(
1
cos
(
θ
)
⋅
1
sin
(
θ
)
)
Multiply
1
cos
(
θ
)
and
1
sin
(
θ
)
.
tan
(
θ
)
1
⋅
1
cos
(
θ
)
sin
(
θ
)
Divide
tan
(
θ
)
by
1
.
tan
(
θ
)
1
cos
(
θ
)
sin
(
θ
)
Rewrite
tan
(
θ
)
in terms of sines and cosines.
sin
(
θ
)
cos
(
θ
)
⋅
1
cos
(
θ
)
sin
(
θ
)
Cancel the common factor of
sin
(
θ
)
.
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1
cos
(
θ
)
⋅
1
cos
(
θ
)
Multiply
1
cos
(
θ
)
and
1
cos
(
θ
)
.
1
cos
(
θ
)
cos
(
θ
)
Raise
cos
(
θ
)
to the power of
1
.
1
cos
1
(
θ
)
cos
(
θ
)
Raise
cos
(
θ
)
to the power of
1
.
1
cos
1
(
θ
)
cos
1
(
θ
)
Use the power rule
a
m
a
n
=
a
m
+
n
to combine exponents.
1
cos
(
θ
)
1
+
1
Simplify the expression.
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1
2
cos
2
(
θ
)
Rewrite
1
2
cos
2
(
θ
)
as
(
1
cos
(
θ
)
)
2
.
(
1
cos
(
θ
)
)
2
Convert from
1
cos
(
θ
)
to
sec
(
θ
)
.
sec
2
(
θ
)
Answer:
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