Respuesta :
[tex]sin^{2}[/tex]theta= 1-[tex]cos^{2}[/tex]theta, so you can simplify the top to that. From there, since that is a difference of squares, you can then factor it to (1-cos theta)(1+cos theta), then cancel out (1+cos theta) on the top and bottom of the fraction so that it becomes C, 1-cos theta.
The simplified ways of the trigonometric expression sin^2 theta/1+cos theta is 1-cos theta. Option C is correct.
What is the simplified form of a term?
Simplified form of a term is the simplest way of expression the term, which is obtained by applying the required operations of mathematics.
The trigonometric expression given in the problem is,
[tex]\dfrac{\sin^2 \theta}{1+\cos \theta }[/tex]
In trigonometric, the value of sin²θ is equal to the (1-cos² θ). Thus,
[tex]\dfrac{1-\cos^2\theta}{1+\cos \theta }[/tex]
Using the formula of square of difference,
[tex]\dfrac{1^2-\cos^2\theta}{1+\cos \theta }\\\dfrac{(1-\cos\theta)(1+\cos\theta)}{1+\cos \theta }\\1-\cos\theta[/tex]
Hence, the simplified ways of the trigonometric expression sin^2 theta/1+cos theta is 1-cos theta. Option C is correct.
Learn more about the simplified form here;
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