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
Answer:
54
Step-by-step explanation:
5 because u subtract u do the adding subject
Each piece is defined over some (limited) domain. When you are evaluating or graphing a piecewise function, you only evaluate or graph the function whose domain includes the variable value of interest.
Given pair of lines are x² + 4xy + y² = 0
⇒ (y/x) ² + 4 y/x + 1 = 0
⇒ y/x = -4±2√3/2 = -2±√3,
∴ The lines y = (-2 + √3) x and y = (-2 - √3) x and x - y = 4 forms an equilateral triangle
Clearly the pair of lines x² + 4xy +y² = 0 intersect at origin,
The perpendicular distance form origin to x - y = 4 is the height of the
h = 2 √ 2
∵ Area of triangle = h²/√3 = 8/√3
