Question

Cot 10° . cot 20°. cot 70°. cot 80°. cot 45° = 1​

Answer 1

Answer:

steps below

Step-by-step explanation:

cot 10° * cot 20° * cot 70° * cot 80° * cot 45°

= (cos 10°/sin 10°)*(cos 20°/sin 20°)*(cos 70°/sin 70°)*(cos 80°/sin 80°)* (1)

= (cos 10°*cos 80°)(cos 20°*cos 70°) / (sin 10°*sin 80°)(sin 20°*sin 70°)

= (1/2*(cos60°+cos90°)*1/2(cos50°+cos90°))/(1/2*(cos60°-cos90°)*1/2(cos50°-cos90°))    ... cos90° = 0     cos60° = 1/2

= (1/8*cos50°) / (1/8*cos50°)

= 1