Quizzes Tests x eTetbook offers l students l MATH 11280 Pla

Quizzes & Tests x eTetbook offers l students l MATH 112-80 Plane Tngonometry Fall 2016 e Take a Test-Edward White-Internet Explorer P https //www.mattad.com/student/playerTestaspartestida 139nussoseerterwin yes MATH 112-80 Plane Tngonometry Fall 2016 Edward White Test: Final Exam This Question: 1 pt 33 of 45 (16 complete) v This Test 4 Tests Verify the identity. Tests sin 5x sin 3x tan (4) cos 5x cos 3x apter 1 F Start with the numerator of the let side and apply the appropriate formula of sumtoproduct sin 5x sin 3x roo not simpler) Now use the sum to-product formula on the denominator of left side ction 1.1 cos 5x cos 3x (Do not simplify.) neexpressions. In the numerator and denominator, substitute the expressions lundin previous steps Apply an appropriate identtytosimpati The fraction from the previous step then simplnes lo tan (Majusing what? ection 1.4 o A. O B. Quotient idently chapter 1 OC Reciprocal ldentity chapter 21 cack to select your Section 21

Solution

sin5x + sin3x

Use sinA + sinB = 2 cos[(A-B)/2] sin[(A+B)/2]

So, sin5x + sin3x = 2cos(x)sin(4x)

cos5x + cos3x

Use cosA + cosB = 2cos(A+B)/2*cos(A -B)/2

cos5x + cos3x = 2cos4xcosx

Now ( sin5x + sin3x)/(cos5x + cos3x ) = 2cos(x)sin(4x)/2cos4xcosx

= sin4x/cos4x

= tan4x   ( by pythogorean identity)