The simplified trigonometric expression is given as follows:
[tex]-sin{\theta}\tan{\theta}(1 - \csc{\theta})[/tex]
How to simplify the given trigonometric expression?
The expression is given by:
[tex]\frac{\cos{\theta}}{1 + \csc{\theta}} \times \frac{1 - \csc{\theta}}{1 - \csc{\theta}}[/tex]
Applying the subtraction of perfect squares at the denominator, we have that the expression is given by:
[tex]\frac{\cos{\theta}(1 - \csc{\theta})}{1 - \csc^2{\theta}}[/tex]
Applying an identity, we have that:
[tex]1 - \csc^2{\theta} = -\cot^2{\theta}[/tex]
Hence the expression is:
[tex]-\frac{\cos{\theta}(1 - \csc{\theta})}{\cot^2{\theta}}[/tex]
cot = cos/sin, hence:
[tex]-\frac{sin^2{\theta}(1 - \csc{\theta})}{\cos{\theta}}[/tex]
tan = sin/cos, hence the simplified expression is:
[tex]-sin{\theta}\tan{\theta}(1 - \csc{\theta})[/tex]
More can be learned about trigonometric expressions at https://brainly.com/question/24496175
#SPJ1
