Simplify the trigonometric expression: (sin 3θ + sin θ) / (cos 3θ + cos θ)

Welcome back Dany — missed you this week. Step 1: Apply the sum-to-product identities to the numerator and denominator. The sum-to-product identities are: A + B = 2 ((A+B)/(2)) ((A-B)/(2)) A + B = 2 ((A+B)/(2)) ((A-B)/(2)) For the numerator, let A = 3 and B = : 3 + = 2 ((3+)/(2)) ((3-)/(2)) = 2 ((4)/(2)) ((2)/(2)) = 2 2 For the denominator, let A = 3 and B = : 3 + = 2 ((3+)/(2)) ((3-)/(2)) = 2 ((4)/(2)) ((2)/(2)) = 2 2 Step 2: Substitute the simplified expressions back into the original fraction. ( 3 + )/( 3 + ) = (2 2 )/(2 2 ) Step 3: Simplify the expression. Cancel out the common terms 2 and (assuming ≠ 0): (2 2 )/(2 2 ) = ( 2)/( 2) Step 4: Use the identity x = ( x)/( x). ( 2)/( 2) = 2 Thus, we have shown that ( 3 + )/( 3 + ) = 2. The final answer is Shown. Send me the next one 📸