Find the value of the following expression:

• cos (360 - A) / sin (270 + A) + cot (90 + A) / tan (180 - A) + sin (90 - A) / sin (90 + A)

To solve the expression cos(360 - A) / sin(270 + A) + cot(90 + A) / tan(180 - A) + sin(90 - A) / sin(90 + A), we can simplify each term step by step.

Breaking Down the Terms

First Term: cos(360 - A) / sin(270 + A)

Using the cosine and sine properties:

• cos(360 - A) = cos(A)
• sin(270 + A) = -cos(A)

Thus, the first term simplifies to:

cos(A) / -cos(A) = -1

Second Term: cot(90 + A) / tan(180 - A)

Using trigonometric identities:

• cot(90 + A) = -tan(A)
• tan(180 - A) = -tan(A)

This gives us:

-tan(A) / -tan(A) = 1

Third Term: sin(90 - A) / sin(90 + A)

Applying sine properties:

• sin(90 - A) = cos(A)
• sin(90 + A) = cos(A)

Therefore, the third term simplifies to:

cos(A) / cos(A) = 1

Final Calculation

Now, we can combine all the simplified terms:

-1 + 1 + 1 = 1

Final Result

The value of the expression is 1.