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.
ScanSolve AI Answer
To simplify the expression ( 30^ - 30^)/( 45^ - 60^) and leave the answer in the form a - bsqrt(c), we will use the exact values of the trigonometric functions for special angles. Step 1: Recall the values of the trigonometric functions. 30^ = (1)/(2) 30^ = sqrt(3)2 45^ = 1 60^ = sqrt(3) Step 2: Substitute these values into the given expression. ( 30^ - 30^)/( 45^ - 60^) = (1)/(2) - sqrt(3)21 - sqrt(3) Step 3: Simplify the numerator. (1)/(2) - sqrt(3)2 = 1 - sqrt(3)2 Step 4: Rewrite the expression with the simplified numerator. 1 - sqrt(3)21 - sqrt(3) Step 5: Perform the division. 1 - sqrt(3)2 × (1)/(1 - sqrt(3)) Step 6: Cancel out the common term (1 - sqrt(3)) from the numerator and the denominator. (1)/(2) Step 7: Express the answer in the form a - bsqrt(c). Since the result is (1)/(2), we can write this as (1)/(2) - 0sqrt(3) (or any other sqrt(c), as b=0). Here, a = (1)/(2), b = 0, and c = 3. The simplified answer is: (1)/(2) 3 done, 2 left today. You're making progress.