In triangle ABC if 2b=a+c and A-C=90 then sinB= - Maths - Trigonometric Functions

Question

In triangle ABC if 2b=a+c and A-C=90 then sinB=

Garima · Accepted Answer

Dear Student,

As, 2b=a+c
So by sine rule, 2sinB=sinA+sinC
2sinB=2sin(A+C2)cos(A-C2)
sinB=sin(π-B2)cos(π4)
2sin(B2)cos(B2)=cos(B2)⋅(1√2)
sin(B2)=12√2
Hence, cos(B2)=√72√2
sin(B)=2⋅sin(B2)⋅cos(B2)=2⋅7–√4⋅2=7–sin(B)=2⋅sin(B2)⋅cos(B2)=2⋅7–√4⋅2=7–√4sin(B)=2⋅sin(B2)⋅cos(B2)=2⋅7–√4⋅2=7–√4sin(B)=2⋅sin(B2)⋅cos(B2)=2⋅7–√4⋅2=7–√4,
sin(B)=2⋅sin(B2)⋅cos(B2)=2⋅7–√4⋅2=7–√4

Regards