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
let's simplify this trigonometric expression without a calculator. 7.3 We need to simplify the expression: ((180^ + x) (x - 360^) 38^)/((360^ + x) 240^ 225^ 412^) Step 1: Simplify each trigonometric term in the numerator. • (180^ + x) = - x (Sine is negative in the third quadrant) • (x - 360^) = x (Tangent has a period of 180^ or 360^) • 38^ remains as is for now. Step 2: Simplify each trigonometric term in the denominator. • (360^ + x) = x (Tangent has a period of 360^) • 240^ = (180^ + 60^) = -60^ = -(1)/(2) (Cosine is negative in the third quadrant) • 225^ = (180^ + 45^) = 45^ = 1 (Tangent is positive in the third quadrant) • 412^ = (360^ + 52^) = 52^ (Sine has a period of 360^) Step 3: Substitute the simplified terms back into the original expression. ((- x)( x)(38^))/(( x)(-1)2)(1)(52^) Step 4: Cancel common terms and simplify the expression. Cancel x from the numerator and denominator (assuming x 0): (- x 38^)/(-1)2 52^ The negative signs cancel out: ( x 38^)/(1)2 52^ Step 5: Use the co-function identity (90^ - ) = . We know that 52^ = (90^ - 38^) = 38^. Substitute this into the expression: ( x 38^)/(1)2 38^ Cancel 38^ from the numerator and denominator (assuming 38^ 0): ( x)/(1)2 2 x The simplified expression is 2 x. What's next?