Question

In a triangle ABC, If `(sin "A" - sin "C")/(cos "C" - cos "A")` = cot B, then A, B, C are in ________.

पर्याय

• Geometric progression

• Arithmetic progression

• Arithmetico-Geometric progression

• Harmonic progression

Answer 1

In a triangle ABC, If `(sin "A" - sin "C")/(cos "C" - cos "A")` = cot B, then A, B, C are in Arithmetic progression.

Explanation:

We have,

`(sin "A" - sin "C")/(cos "C" - cos "A")` = cot B

`=> (2 cos (("A + C")/2) sin ("A - C")/2)/(2 sin (("C + A")/2) sin (("A - C")/2))` = cot B

`=> cot (("A + C")/2)` = cot B

⇒ A + C = 2B

∴ A, B, C are in Arithmetic progression.