Express the given sum or difference as a product of sines an

Express the given sum or difference as a product of sines and/or cosines. sin 90 sin 0 sin 90 sin 0 (Simplify your answer, including any radicals. Use integers or fractions for any num

Solution

sin 9 theta - sin theta

applying difference to product formula

sin a - sin b = 2 {sin (a-b)/2 cos (a+b)/2}

therefore,

sin 9 theta - sin theta = 2 { sin (9 theta - theta )/2 cos (9 theta + theta )/2 }

= 2 { sin 4 theta * cos 5 theta }