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
Here are the solutions: 2.1.1) Step 1: Use the reduction formula for sine in the fourth quadrant, (360^ - ) = - . Step 2: Express 335^ as 360^ - 25^. 335^ = (360^ - 25^) Step 3: Apply the reduction formula. 335^ = - 25^ 2.1.2) Step 1: Use the double angle identity for cosine, (2) = 1 - 2^2 . Step 2: Let 2 = 50^, so = 25^. 50^ = (2 × 25^) Step 3: Apply the double angle identity. 50^ = 1 - 2^2 25^ 2.2) Step 1: Simplify each term in the expression using trigonometric identities. • (-2x) = -(2x) (odd function identity) • 1 - ^2 x = ^2 x (Pythagorean identity) • (90^ + x) = x (co-function identity) • x = ( x)/( x) (quotient identity) Step 2: Substitute these simplified terms into the expression. ((-2x) · (1 - ^2 x))/((90^ + x) · x) = (-(2x) · ^2 x)/( x · x) x Step 3: Simplify the denominator. (-(2x) · ^2 x)/( x) Step 4: Apply the double angle identity for sine, (2x) = 2 x x. (-(2 x x) · ^2 x)/( x) Step 5: Cancel out x from the numerator and denominator (assuming x ≠ 0). -2 x · ^2 x Step 6: Combine the cosine terms. -2^3 x That's 2 down. 3 left today — send the next one.