Solve: cot 7 /16 + 2cot 3 /8 + cot 15 /16 - Maths - Trigonometric Functions

Question

Solve:
cot 7 π /16 + 2cot 3 π /8 + cot 15 π /16

Ghanshyam Dhakar · Accepted Answer

Dear
student,

cot7π16+cot15π16+2cot3π8=cot7π16+cotπ-π16+2cot3π8use cotπ-x=-cotxcot7π16-cotπ16+2cot3π8use cotx= cosxsinx=cos7π16sin7π16-cosπ16sinπ16+2cot3π8=sinπ16cos7π16-sin7π16cosπ16sinπ16sin7π16+2cot3π8use sina-b= sina cosb-cosa sinb=2sinπ16-7π162sinπ16sin7π16+2cot3π8use cosa-b-cosa+b = 2sinasinb=-2sin3π8cosπ16-7π16-cosπ16+7π16+2cot3π8=-2sin3π8cos3π8-cosπ2+2cot3π8=-2sin3π8cos3π8+2cos3π8sin3π8=2cos23π8-sin23π8sin3π8cos3π8use cos2x-sin2x = cos2x=4cos3π42sin3π8cos3π8=4cos3π4sin3π4==4cot3π4 =4cotπ-π4=-4cotπ4=-4
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Solve: cot 7 π /16 + 2cot 3 π /8 + cot 15 π /16

Solve:
cot 7 π /16 + 2cot 3 π /8 + cot 15 π /16