1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In Δ ABC the sides opposite to angles A,B,C are denoted by a,b,c respectively.If 2b2=a2+c2, then sin3BsinB is equal to?

A
c2a22ca
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
c2a2ca
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(c2a2ca)2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(c2a22ca)2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct options are A c2−a22ca C (c2−a2ca)2 D (c2−a22ca)2sin3BsinB=3sinB−4sin3BsinB=3−4sin2BGiven, 2b2=a2+c2We Know, cosB=a2+c2−b22ac⇒2b2−b22ac[CosineRule]cosB=b22acsinB=√1−(b22ac)2[∵sin2B+cos2B=1]sin3BsinB=3−4[(1−b22ac)]2=⎡⎣(b2)2(2ac)2−1⎤⎦=b4−4a2c24a2c2sin3BsinB=(a2+c22)2−4a2c24a2c2=(a2−c22ca)2Hence, c2−a22ca, (c2−a2ca)2, (c2−a22ca)2 are the correct answers.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Factorisation and Rationalisation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program