prove that tan^pi/16 + tan^2pi/16 +.........+tan^7pi/16 = 35 Share with your friends Share 21 Priyanka Kedia answered this 7π16=π2-π166π16=π2-2π165π16=π2-3π164π16=π4L.H.S.=tan2π16+tan22π16+tan23π16+tan24π16+tan25π16+tan26π16+tan27π16 =tan2π16+tan22π16+tan23π16+tan2π4+tan2π2-3π16+tan2π2-2π16+tan2π2-π16 =tan2π16+tan22π16+tan23π16+1+cot23π16+cot22π16+cot2π16 =tan2π16+cot2π16+1+cot22π16+tan22π16+tan23π16+cot23π16 Solve first bracket,tan2π16+cot2π16=tanπ16+cotπ162-2tanπ16cotπ16 =sinπ16cosπ16+cosπ16sinπ162-2 =1sinπ16cosπ162-2 =22sinπ16cosπ162-2 =2sinπ82-2 =81-cosπ4-2 =822-1-2 =822+1-2Similarly, 2nd bracket=81-cosπ2-2=8-2=6And, 3rd bracket=81-cos3π4=822-1-2Thus, equation 1 becomes,L.H.S.=822+1-2+6+1+822-1-2=35=R.H.S.Hence Proved. 91 View Full Answer