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
Step 1: Simplify ( )/( ). Using the quotient identity, we have: ( )/( ) = The correct option is 1. The final answer is 1) . Step 2: Simplify (1 + ^2 ). Using the Pythagorean identity, we have: 1 + ^2 = ^2 The correct option is 1. The final answer is 1) ^2 . Step 3: Find the value of (60^). We know that (60^) = sqrt(3). Since = (1)/( ): (60^) = (1)/((60^)) = (1)/(sqrt(3)) The correct option is 3. The final answer is 3) (1)/(sqrt(3)). Step 4: Find the value of (90^). We know that = (1)/( ). Since (90^) = 0: (90^) = (1)/((90^)) = (1)/(0) The value is undefined. The correct option is 3. The final answer is 3) undefined. Step 5: If () = sqrt(3), find . We know that (60^) = sqrt(3). Therefore: = 60^ The correct option is 3. The final answer is 3) 60^. Step 6: If = (3)/(5) and is acute, find . Using the Pythagorean identity ^2 + ^2 = 1: ((3)/(5))^2 + ^2 = 1 (9)/(25) + ^2 = 1 ^2 = 1 - (9)/(25) ^2 = (25 - 9)/(25) ^2 = (16)/(25) = ± sqrt((16)/(25)) = ± (4)/(5) Since is acute (in the first quadrant), must be positive. = (4)/(5) The correct option is 1. The final answer is 1) (4)/(5). Step 7: If - = 0, find . Given the equation: = 0 = Divide both sides by (assuming ≠ 0): ( )/( ) = 1 = 1 We know that (45^) = 1. Therefore: = 45^ The correct option is 2. The final answer is 2) 45^. Step 8: If ( - ) = x, find ( + ). Using the Pythagorean identity ^2 - ^2 = 1. Factor the left side as a difference of squares: ( - )( + ) = 1 Substitute the given value ( - ) = x: x( + ) = 1 Solve for ( + ): + = (1)/(x) The correct option is 1. The final answer is 1) (1)/(x). Step 9: Find the value of (1 - ^2 )/(1 + ^2 ). This is the double angle formula for cosine: (1 - ^2 )/(1 + ^2 ) = (2) The correct option is 1. The final answer is 1) (2). Send me the next one 📸