David proved the law of cosines with reference to ∆abc using a different method. arrange the steps of his proof in the correct sequence. in , (pythagorean theorem) in , (pythagorean theorem) (on simplification) (transitive property) therefore, . similarly, prove that and . (on simplification) (on simplification) draw a perpendicular, , from b to side ac. let and . therefore, .

We can arrange the steps with help of below explanation.  

Step-by-step explanation:

Here ABC is a triangle,

Draw a perpendicular from BD to side AC ( construction)

where

In the right triangle BCD, from the definition of cosine:

cos C =CD/ BC

CD= a cos C

Subtracting this from the side b, we see that

DA=b-acos C  

In the triangle BCD, from the definition of sine:

sin C =BD  / a

BD = a sin C  

In the triangle ADB, applying the Pythagorean Theorem

Substituting for BD and DA from (2) and (3)

⇒   ( On simplification)

⇒

⇒

⇒ (because, )