Is it possible to factor 1 − sin two different ways? If so, show and explain. If not, why not?
Answers
Step-by-step explanation:
1
−
sin
2
(
x
)
Rewrite
1
as
1
2
.
1
2
−
sin
2
(
x
)
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
1
and
b
=
sin
(
x
)
.
Answer:
Step-by-step explanation:
As per the data given in this question
we have to show and explain, the factor for 1-sin2x in two different ways.
Yes, it is possible to factor 1-sin2x.
Explanation:
Here are two different ways to factor 1-sin2x:
The first way to factor 1-sin2x is:
As per the trigonometric identities we know that :
- 1-sin2x = cos x^{2} +sin x^{2} - sin2x
= cos x^{2} +sin x^{2} - 2sinx.cosx
= (cos x- sin x) ^{2}
[ Since, as we know that sin x^{2} +cos x^{2} =1 and sin2x=2sinxcosx]
The second way to factor 1-sin2x is:
As per the trigonometric identities we know that :
- 1-sin2x = sin x^{2} +cos x^{2} - sin2x
= sin x^{2} +cos x^{2} -2sinx.cosx
= (sin x-cos x)^{2}
In the above equation as we can see that the two different ways to solve the factor for 1-sin2x.
So, it is possible to factor 1-sin2x.
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