Question

For any triangle show the sin theorem.
show that,

pls someone help me​

Answer 1

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