Simplify the expression: [cos(90° + A) / sec(270° - A)] + [sin(270° + A) / cosec(630° - A)].

Introduction / Context:
This question tests trigonometric angle-shift identities (90°, 270°, 630°) and reciprocal functions (sec, cosec). These angles are designed so that everything reduces to simple sin A and cos A terms. After simplification, the expression becomes sin^2 A + cos^2 A, which is always 1.

Given Data / Assumptions:

• Expression: cos(90° + A)/sec(270° - A) + sin(270° + A)/cosec(630° - A)
• Identities:
  • cos(90° + A) = -sin A
  • sin(270° + A) = -cos A
  • sec x = 1/cos x
  • cosec x = 1/sin x
  • cos(270° - A) = -sin A
  • sin(630° - A) = sin(360° + 270° - A) = sin(270° - A) = -cos A

Concept / Approach:
Rewrite each trig function using standard shift identities, convert sec and cosec into cos and sin, then simplify each fraction separately and add.

Step-by-Step Solution:

Verification / Alternative check:
Take A = 0: first term becomes cos90/sec270 = 0/undefined? but through simplified identity form it becomes sin^2 0 = 0 and second term becomes cos^2 0 = 1, total 1 (valid where defined). The identity result remains 1 wherever the original expression is defined.

Why Other Options Are Wrong:

Common Pitfalls:
Mis-evaluating 270° shifts (sign errors), and forgetting that sec and cosec are reciprocals, not independent functions.

Final Answer:
1