Question

Prove that :cos36*cos42*cos60*cos78=1/16.....plz help me out

Answer 1

Answer:

Step-by-step explanation:

cos36*cos42*cos60*cos78 = 1/16

//first multiply and divide by 2

[1/2] cos36 * cos60 * [2cos42*cos78]

//Remember: 2cosAcosB = Cos(A+B) + Cos(A-B)

= (1/2)cos36* cos60*[Cos120°+Cos36°]

//cos36° = (√5 + 1)/4

= (1/2)[(√5+1)/4](1/2)[-1/2+(√5+1)/4]

= (√5+1)/16 * [-1/2+(√5+1)/4]

= (√5+1)/16 * (√5-1)/4

= 5-1/64

= 4/64 = 1/16