Step-by-step explanation:
cot A + cot C
Write in terms of sine and cosine:
cos A / sin A + cos C / sin C
Common denominator:
(cos A sin C + cos C sin A) / (sin A sin C)
Angle sum formula:
sin(A+C) / (sin A sin C)
Angles of a triangle add up to π:
sin(π−B) / (sin A sin C)
Shift identity:
sin B / (sin A sin C)
Law of sines:
sin B / ((a sin B / b) × (c sin B / b))
sin B / (ac sin² B / b²)
b² / (ac sin B)
From law of cosine:
b² = a² + c² − 2ac cos B
b² = 2b² − 2ac cos B
b² = 2ac cos B
b² / (ac) = 2 cos B
Substituting:
2 cos B / sin B
2 cot B
