Using standard trigonometric identities and values, evaluate the expression (sec^2 45 degrees - cot^2 45 degrees) - (sin^2 30 degrees + sin^2 60 degrees) and then select the correct simplified result from the options.

Introduction / Context:
This problem tests your familiarity with special angle values and basic trigonometric identities. You need to substitute exact values for 30 degrees, 45 degrees, and 60 degrees, square them where required, and then perform straightforward arithmetic to obtain the final simplified value of the expression.

Given Data / Assumptions:

• The expression is (sec^2 45 degrees - cot^2 45 degrees) - (sin^2 30 degrees + sin^2 60 degrees).
• We use exact values for trigonometric functions at standard angles.
• All calculations are done with real numbers.
• No calculators or decimal approximations are necessary.

Concept / Approach:
First recall sin, cos, and tan values for 30 degrees, 45 degrees, and 60 degrees. From these you can find sec and cot as reciprocals of cos and tan respectively. Then square the relevant quantities, carefully apply the minus signs, and finally combine the results into one simplified number.

Step-by-Step Solution:
Use standard values: sin 30 degrees = 1/2, sin 60 degrees = √3/2, tan 45 degrees = 1, cos 45 degrees = √2/2. From cos 45 degrees = √2/2, sec 45 degrees = 1 / cos 45 degrees = √2, so sec^2 45 degrees = 2. From tan 45 degrees = 1, cot 45 degrees = 1, so cot^2 45 degrees = 1. Compute sin^2 30 degrees = (1/2)^2 = 1/4 and sin^2 60 degrees = (√3/2)^2 = 3/4, so sin^2 30 degrees + sin^2 60 degrees = 1. Now evaluate the expression: (sec^2 45 - cot^2 45) - (sin^2 30 + sin^2 60) = (2 - 1) - 1 = 1 - 1 = 0.
Verification / Alternative check:
You can see that sec^2 45 degrees - cot^2 45 degrees simplifies to 1, and sin^2 30 degrees + sin^2 60 degrees also simplifies to 1. Therefore the overall expression is 1 - 1. This equality provides a quick mental check without redoing all intermediate steps in detail.

Why Other Options Are Wrong:
Option a ( 1 ) corresponds to keeping only the first bracket and forgetting the subtraction of the second bracket. Option c ( 1/√2 ) and option d ( 2√3 ) are not consistent with squaring the functions and represent confusion with unsquared values. Option e ( -1 ) would arise from an incorrect sign arrangement or miscalculation of the individual squares.

Common Pitfalls:
Learners sometimes forget to square the trigonometric values or they square only the number but not the entire function. Another common mistake is to approximate surds and then introduce rounding errors. Keeping everything symbolic and using known exact values avoids these issues.

Final Answer:
The simplified value of the given trigonometric expression is 0.