1. Derive this identity from the sum and difference formulas for cosine: sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]Calculation:1. 2. 3. Reason:1.2.3.2. Use the trigonometric subtraction formula for sine to verify this identity:sin((π / 2) – x) = cos xCalculation: 1. 2. 3. Reason:1.2.3.
Accepted Solution
A:
Answer:See below.Step-by-step explanation:1. (1 / 2)[cos(a – b) – cos(a + b)]= 1/2 ( cosa cosb + sina sinb - (cosa cosb - sina sinb)= 1/2 ( cosa cosb - cosa cos b + sina sinb + sina sinb)= 1/2 ( 2 sina sinb)= sina sinb.(I used the 2 identities cos(a - b) = cosa cosb + sina sinb) andcos (a + b) = cosa cosb - sina sinb.)2. sin (π/2 - x) = sin (π/2) cos x - cos(π/2) sin x = 1 * cos x - 0 * sinx = cosx - 0 = cos x. (I used the identity sin(a - b) = sina cosb - cosa sinb and the fact that sin(π/2) = 1 and cos (π/2) = 0. )