Question

prove that cot pi by 16.cot 2 pi by 16. cot 3 pi 16....cot 7 pi by 16=1​

Answer 1

Answer:

(π/16) * cot (2π/16) * cot (3π/16) * … *cot (7π/16) = 1

LHS = cot(π/16) * cot (2π/16) * cot (3π/16) *cot (4π/16) * cot (5π/16) * cot (6π/16) *cot

(7π/16)

= cot(π/16) * cot (2π/16) * cot (3π/16) *cot (π/4) * cot (8π/16–3π/16) * cot (8π/16–2π/16) *cot (8π/16-π/16)

=cot(π/16) * cot (2π/16) * cot (3π/16) *cot (π/4) * cot (π/2–3π/16) * cot (π/2–2π/16) *cot (π/2-π/16)

=cot(π/16) * cot (2π/16) * cot (3π/16) *cot (π/4) * tan(3π/16) * tan(2π/16) * tan(π/16)

=cot(π/16) * tan(π/16) * cot (2π/16) * tan(2π/16)* cot (3π/16)* tan(3π/16) *cot (π/4) =1*1*1*1

=1=RHS