Question

If B=30° prove that, 3 sin B - 4sin² B= sin 3 B.
please answer this question.
no franks​

Answer 1

Answer:

•cosA+cosB=4sin

2

(

2

C

)

2cos

2

A+B

cos

2

A−B

=4sin

2

(

2

C

)

A+B+C=π⇒A+B=π−C

cos

2

π−C

cos

2

A−B

=2sin

2

(

2

C

)

sin

2

C

cos

2

A−B

=2sin

2

(

2

C

)

cos

2

A−B

=2sin(

2

C

)

cos

2

C

cos

2

A−B

=2sin(

2

C

)cos

2

C

cos(

2

π−(A+B)

)cos

2

A−B

=sinC

2sin

2

A+B

cos

2

A−B

=sinC

sinA+sinB=2sinC

a

sinA

=

b

sinB

=

c

sinC

=k

sinA=ak,sinB=bk,sinC=ck

ak+bk=2(ck)

a+b=2c

Therefore the sides of triangle a,b,c are in A.P.