prove that cos of pi by 5 *cos of 2pi by 5*cos of 4pi by 5*cos of 8pi by 5 - Maths - Trigonometric Functions

Question

prove that cos of pi by 5 *cos of 2pi by 5*cos of 4pi by 5*cos of
8pi by 5 =-1/16

Mayank · Accepted Answer

We have,cosπ5 = 5+14cos2π5 = 5-14cos4π5 = -5+14cos8π5 = 5-14LHS = cosπ5×cos2π5×cos4π5×cos8π5=5+14 × 5-14 × -5+14 × 5-14=-5+12 5-1216 × 16=-116 = RHS

prove that cos of pi by 5 *cos of 2pi by 5*cos of 4pi by 5*cos of 8pi by 5 =-1/16