Question

The point on the line 2x-3y+7=0 whose abscissa is 5/2 times the ordinate is​

Answer 1

(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

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