Find the exact value please show all work a sin 36cos 24sin

Find the exact value (please show all work)

a. sin 36°cos 24°-sin 24°cos°36

b. pi/12

c. sin 75°

Solution

a) we have given sin 36⁰cos 24⁰-sin 24⁰cos36⁰

sin 36⁰cos 24⁰-sin 24⁰cos36⁰=sin(36⁰-24⁰)=sin(12⁰)=0.20791169081

b) pi/12=0.26179938779

c) sin75⁰=sin(45⁰+30⁰)=sin45⁰cos30⁰+cos45⁰sin30⁰=1/sqrt(2)*(sqrt(3)/2)+1/sqrt(2)*1/2 =(sqrt(3)+1)/2sqrt(2)

sin75⁰=(1+sqrt(3))/(2*sqrt(2))