Question

cos π\12 × cos π\6 × cos π\3 × cos5π\12 = √3/16​

Answer 1

L H S

= cos π/12×cos π/6×cosπ/3× cos 5π/12

= cos( π/4 - π/6) × √3/2×1/2×cos( π/4+π/6)

√3/4×[ cos π/4 cos π/6+ sin π/4 sin π/6]

× [ cos π/4 cos π/6- sin π/4 sinπ/6]

=> √3/4[ ( 1/√2× √3/2)²- ( 1/√2× 1/2)²]

formula used

cos( A+B)= cosAcosB- sinAsinB

cos(A-B)= cosAcosB+ sinAsinB

(a+b) ( a-b)= a²- b²

again

√3/4×[ ( 1/2×3/4) - ( 1/2×1/4)

= √3/4[ 3/8 - 1/8]

= √3/4× 1/4

= √3/16

= R H S