Question

cos²π/12+cos²π/4+cos²5π/12​

Answer 1

cos²5π/12+cos²(π/12+5π/12)+cos5π/12×cosπ/12

=cos²(3π/12+2π/12)+cos²π/2+cos(3π/12+2π/12)×cos(3π/12-2π/12)

=cos²(π/4+π/6)+cos(π/4+π/6)×cos(π/4-π/6)

=cos(π/4+π/6)[cos(π/4+π/6)+cos(π/4-π/6)]

=(√6-√2)/4[(√6-√2)/4+(√6+√2)/4]

=(√6-√2)/4x(√6/2)

=(6-2√3)/8

=(3-√3)/4

Hope it helps .............✌