This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Question 73: If is an angle, then ^2 + (1+)(1-) = ? Step 1: Simplify the product (1+)(1-). This is a difference of squares, which follows the formula (a+b)(a-b) = a^2 - b^2. Here, a=1 and b=. (1+)(1-) = 1^2 - ()^2 = 1 - ^2 Step 2: Substitute this simplified term back into the original expression. The expression becomes: ^2 + (1 - ^2) Step 3: Use the Pythagorean trigonometric identity. Recall the identity: ^2 = 1 + ^2. Step 4: Substitute ^2 with 1 + ^2 in the expression. (1 + ^2) + (1 - ^2) Step 5: Combine like terms. 1 + ^2 + 1 - ^2 (1+1) + (^2 - ^2) 2 + 0 2 The value of the expression is 2. Step 6: Compare the result with the given options. A. -1 B. 0 C. 1 D. 2 The calculated value matches option D. The final answer is D. 2.