Question

tan20°tan40°tan45°tan50°tan70°=1

Answer 1

tan20=cot70

tan40=cot50.

Since cot70cot50tan45tan50tan70.

1=RHS

Answer 2

LHS = tan20°. tan40°. tan45°. tan50°. tan70°

we know,
tan(90 - A) = cotA

so, tan20° = tan(90° - 70°) = cot70°

tan40° = tan(90° - 50°) = cot50°

and also we know tan45° = 1

= (cot70°).(cot50°). 1 . tan50° . tan70°

= {tan70° . cot70°}. {tan50°. cot50°}

= 1 . 1 = 1 = RHS