Question

Prove that cos36*cos72 = 1/2

Answer 1

try looking into the standard angles tables

Answer 2

Step-by-step explanation:

cos36 - cos72

cos36-cos72= (cos²36-cos²72)/cos36

so from identity cos²x=(cos2x+1)/2

so cos36-cos72=cos72+1-(cos144+1)/2(cos36+cos72

which is equal to 1/2

or using

cos36-cos72=cos36-cos2(36)

and from identity cos2x=2cos²x-1

so cos36-cos72=cos36-(2cos²36-1)=cos36-2cos²36+1

and we know cos36 to be (√5 + 1)/4

so cos36-cos72=(√5 + 1)/4 - 2((√5 + 1)/4)² +1

which is equal to (√5 + 1)/4 - 2((5 + 2√5 + 1)/16)) + 1

which is equal to (√5 + 1)/4 -2(2(3 + √5)/16)) + 1

so equals (√5 + 1)/4 - ((3 + √5)/4)) + 1

which is equal to (√5 + 1 -3 - √5 + 4)/4

which is equal to 2/4 = 1/2

proved

I hope this helps