Question

In∆ABC prove that a²=b²+c²-2bc cos A
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Answer 1

Step-by-step explanation:

I hope you this answer is correct

Answer 2

Given,

ABC is a triangle.

To Find,

Prove that a²=b²+c²-2bc cos A.

Solution,

ΔABC is a triangle.

In this a vector+ b vector+ c vector=0

⇒b vector+ c vector= -a vector

Then, squaring both the sides,

⇒(b vector+ c vector)²= (-a vector)²

⇒(b vector + c vector)(b vector + c vector)=(-a vector)(-a vector)

⇒b vector. b vector+ c vector. b vector + b vector. c vector+ c vector. c vector= (a vector)(a vector)

⇒b²+cb cos(π-A)+bc cos(π-A)+c²=a²(∵we know b vector. b vector=b²)

⇒b²+2bc cos(π-A)+c²=a²

⇒b²+c²-2bc cos A=a²

Hence, proved that a²=b²+c²-2bc cos A.