Respuesta :
She can multiply the numerator and denominator by (1+sin θ).
[tex]\frac{1}{1-\sin \theta} \times \frac{1+\sin \theta}{1+\sin \theta} \\ \\=\frac{1+\sin \theta}{1*1+\sin \theta \times1-\sin \theta \times1 -\sin \theta \times \sin \theta} \\ \\=\frac{1+\sin \theta}{1+\sin \theta -\sin \theta - \sin ^2 \theta} \\ \\=\frac{1+ \sin \theta}{1-\sin ^2 \theta}[/tex]
From our trigonometric identities, we know that 1-sin² θ = cos² θ, so we have:
[tex]\frac{1+\sin \theta}{\cos ^2 \theta}[/tex]
[tex]\frac{1}{1-\sin \theta} \times \frac{1+\sin \theta}{1+\sin \theta} \\ \\=\frac{1+\sin \theta}{1*1+\sin \theta \times1-\sin \theta \times1 -\sin \theta \times \sin \theta} \\ \\=\frac{1+\sin \theta}{1+\sin \theta -\sin \theta - \sin ^2 \theta} \\ \\=\frac{1+ \sin \theta}{1-\sin ^2 \theta}[/tex]
From our trigonometric identities, we know that 1-sin² θ = cos² θ, so we have:
[tex]\frac{1+\sin \theta}{\cos ^2 \theta}[/tex]
She can multiply the numerator and denominator by 1 + sin θ. Then the correct option is D.
What is trigonometry?
Trigonometry deals with the relationship between the sides and angles of a triangle.
The expression is given below.
[tex]\dfrac{1}{1-\sin\theta}[/tex]
Multiply and divide the expression by the 1 + sin θ. Then we have
[tex]\dfrac{1}{1-\sin\theta} \times \dfrac{1+\sin\theta}{1+\sin\theta}\\\\\dfrac{1+\sin\theta}{1-\sin^2\theta}[/tex]
We know that the formula
[tex]1-\sin^2\theta = \cos^2 \theta[/tex]
Then we have
[tex]\dfrac{1+\sin\theta}{\cos^2 \theta}[/tex]
Thus, she can multiply the numerator and denominator by 1 + sin θ.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
