Answer:
The first line of her proof is [tex]\cos\theta \tan\theta =\sin\theta[/tex]
Step-by-step explanation:
The given trigonometric identity is [tex]\cos(-\theta) \tan\theta =\sin\theta[/tex].
Jana has to recall that, the cosine function is an even function.
For that matter, [tex]\cos(-\theta)=\cos(\theta)[/tex].
Jana has to apply this property by substituting [tex]\cos(\theta)[/tex] for [tex]\cos(-\theta)[/tex] in the given identity to obtain,
[tex]\cos\theta \tan\theta =\sin\theta[/tex].
Note that, the sine and the tangent functions are odd functions, therefore,
[tex]\sin(-\theta)=-\sin(\theta)[/tex]
and
[tex]\tan(-\theta)=-\tan(\theta)[/tex]
Hence, the correct answer is option C.
