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Mathematics
Problem
A student attempts to verify the identity
1
−
cos
2
x
sin
x
=
sin
x
\dfrac{1-\cos^{2}x}{\sin x}=\sin x
sin
x
1
−
cos
2
x
=
sin
x
as follows: Step 1:
1
−
cos
2
x
sin
x
=
tan
2
x
sin
x
\dfrac{1-\cos^{2}x}{\sin x}= \dfrac{\tan^{2}x}{\sin x}
sin
x
1
−
cos
2
x
=
sin
x
tan
2
x
Step 2:
=
sin
2
x
sin
x
=\dfrac{\sin^{2}x}{\sin x}
=
sin
x
sin
2
x
Step 3:
=
sin
x
=\sin x
=
sin
x
At which step does the first error occur? a) Step 2 b) There is no error c) Step 1 d) Step 3
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