Question

I have to follow this direction to get the answer. I'm totally stuck

Answer 1

The simplified trigonometric expression is given as follows:

$-sin{\theta}\tan{\theta}(1 - \csc{\theta})$

How to simplify the given trigonometric expression?

The expression is given by:

$\frac{\cos{\theta}}{1 + \csc{\theta}} \times \frac{1 - \csc{\theta}}{1 - \csc{\theta}}$

Applying the subtraction of perfect squares at the denominator, we have that the expression is given by:

$\frac{\cos{\theta}(1 - \csc{\theta})}{1 - \csc^2{\theta}}$

Applying an identity, we have that:

$1 - \csc^2{\theta} = -\cot^2{\theta}$

Hence the expression is:

$-\frac{\cos{\theta}(1 - \csc{\theta})}{\cot^2{\theta}}$

cot = cos/sin, hence:

$-\frac{sin^2{\theta}(1 - \csc{\theta})}{\cos{\theta}}$

tan = sin/cos, hence the simplified expression is:

$-sin{\theta}\tan{\theta}(1 - \csc{\theta})$

More can be learned about trigonometric expressions at https://brainly.com/question/24496175

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