**Problem 2: Using Sum and Difference Formulas**Use sum and difference formulas to find the exact value of each expression.a. \( \sin \frac{\pi}{9} \cos \frac{4\pi}{9} - \cos \frac{\pi}{9} \sin \frac{4\pi}{9} \)b. \( \frac{\tan 40^\circ - \tan 10^\circ}{1 + \tan 40^\circ \tan 10^\circ} \)**Explanation:**- For part (a), the expression follows the sine difference identity: \[ \sin(A - B) = \sin A \cos B - \cos A \sin B \] where \( A = \frac{\pi}{9} \) and \( B = \frac{4\pi}{9} \).- For part (b), the expression follows the tangent difference identity: \[ \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} \] where \( A = 40^\circ \) and \( B = 10^\circ \).

Name: **Problem 2: Using Sum and Difference Formulas**Use sum and differenc
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Problem 2: Using Sum and Difference Formulas**Use sum and difference formulas to find the exact value of each expression.a. \( \sin \frac{\pi}{9} \cos \frac{4\pi}{9} - \cos \frac{\pi}{9} \sin \frac{4\pi}{9} \)b. \( \frac{\tan 40^\circ - \tan 10^\c

a) Sinπ9cos4π9- cosπ9sin4π9 This can be converted in Sin(A-B) As, Sin(A-B) = SinA CosB - CosA SinB Here, A = π9 and B = 4π9Now, putting, A and B in the formula , Hence , Sinπ9cos4π9- cosπ9sin4π9 can be written as =Sin(π9-4π9) = sin(-3π/9) = Sin(-π/3) = - Sin(π/3) = -√3/2 .Hence, Sinπ9cos4π9- cosπ9sin4π9= -√3/2 = -0.866b) Here, a = 40° and b = 10° Hence, the given formula could be written as = Tan ( 40° - 10°) = Tan 30° = 1/√3 = 0.577The answer is = 1/√3 = 0.577 .