Home
Class 12
MATHS
If in DeltaABC,2b^(2)=a^(2)+c^(2), then...

If in `DeltaABC,2b^(2)=a^(2)+c^(2)`, then `(sin3B)/(sinB)` is equal to

A

`(c^(2)-a^(2))/(2ca)`

B

`(c^(2)-a^(2))/(ca)`

C

`((c^(2)-a^(2))/(ca))^(2)`

D

`((c^(2)-a^(2))/(2ca))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(sin3B)/(sinB)=(3sinB-4sin^(3)B)/(sinB)=3-4sin^(2)B`
`=3-4(1-cos^(2)B)`
`=-1+(4(a^(2)+c^(2)-b^(2))^(2))/(4(ac)^(2))`
`=-1+((a^(2)+c^(2))/(2))^(2)/((ac)^(2))`
`[because2b^(2)=a^(2)+c^(2)("given")]`
`=-1+((a^(2)+c^(2))^(2))/(4(ac)^(2))`
`=((a^(2)+c^(2))^(2)-4a^(2)c^(2))/(4(ac)^(2))=((c^(2)-a^(2))/(2ac))^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

In a DeltaABC," if " a^(2)sinB=b^(2)+c^(2) , then :

If the area of a DeltaABC be lambda , then a^(2)sin2B+b^(2)sin2A is equal to

If in a DeltaABC, (a^(2)-b^(2))/(a ^(2)+b^(2))=(sin (A-B))/(sin (A+B)), then the triangle is

If the area of DeltaABC be lamda , then a^(2) sin 2B + b^(2) sin 2A is equal t,o

In DeltaABC,(a-b)^(2)"cos"^(2)(C)/(2)+(a+b)^(2)"sin"^(2)(C)/(2) is equal to

If Delta denotes the area of DeltaABC , then b^(2) sin 2C + c^(2) sin 2B is equal to

If sinB=1/5sin(2A+B), then (tan(A+B))/(tanA) is equal to

lf in DeltaABC,b^(2)sin 2C + c^(2) sin 2B = 2bc,then the triangle is

In any DeltaABC, sum a^(2) (sin^2 B - sin^2 C) =