CGPET 2019 Solved Paper

Given, sin(2A+B)=

1

2

⇒sin(2A+B)=sin‌

5π

6

‌ ⇒2A+B=

5π

6

......(i)
A+B+C=π [angle sum property ] ........(ii)
As, A,B and C are in A.P.

So, B−A=C−B ⇒A−2B+C=0 ........(iii)
From Eqs. (ii) and (iii), we get
B=

π

3

On putting the value of angle B in Eq. (i), we get
2A+

π

3

=

5π

6

⇒2A=

π

2

⇒A=

π

4

On putting thevalue of angles A and B in Eq. (ii), we get

π

4

+

π

3

+C=π⇒C=

5π

12

Hence, (A,B,C) i.e.. (

π

4

,

π

3

,

5π

12

).