Question

Simplifying Trigonometric Expressions-

Simplify the trigonometric expression$\frac{1+\sin y}{1+\csc y}$

Short answer

On simplifying expression we get$\sin y$

Step-by-step solution

Step 1. Given information.

A trigonometric expression as$\frac{1+\sin y}{1+\csc y}$

Step 2. Concept used.

To reduce an equation to its simplest form, we'll apply trigonometric identities. Covert the given expression in simplest form and that form is the correct answer.

Step 3. Calculation.

Now, simplify $\frac{1+\sin y}{1+\csc y}$using identities:

$\frac{1+\sin y}{1+cscy}=\frac{1+\sin y}{1+\frac{1}{\sin y}}$

$\frac{1+\sin y}{1+cscy}=\frac{1+\sin y}{1+\sin y}\times \sin y$

$\frac{1+\sin y}{1+cscy}=\sin y$