Question

Show that Sin (B+C) = cosA/2​

Answer 1

Step-by-step explanation:

by angle sum property

A+B+C=180

B+ C=180-A

dividing both sides by 2

B/2+C/2=180/2-C/2

B/2+C/2=90-C/2

Now,

sinB+C=cos(90-A/2)

sinB+C=sinA/2

Answer 2

Step-by-step explanation:

since A,BandC are the interior angleB of a ∆ABC,

therefore,A+B+C=180°

or, A+B+C

------------- = 90°

2

so, B+C A

--------=90°- ----

2 2

Therfore,sin(B+C) sin(90°-A)

-------= ---------

2. 2

or,sin(B+C) cosA

-------= ---

2 2

Hence prove