Home
Class 12
MATHS
If in a triangle ABC,4sin A = 4 sin B=3...

If in a triangle `ABC,4sin A = 4 sin B=3 sin C`, then `cos C=`

A

`1//3`

B

`1//9`

C

`1//27`

D

`1//18`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `(sinA)/(1//4)=(sin B)/(1//4)=(sin C)/(1//3)`
`:." "(sinA)/(3)=(sinB)/(3)=(sinC)/(4)`
Here, a = 3k, b = 3k and c = 4k, where k is a proportionality constant.
`:.cosC=(9k^(2)+9k^(2)-16k^(2))/(2xx3kxx3k)=(1)/(9)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRACTICE SET 18

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|50 Videos

  • PRACTICE SET 20

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (Mathematics)|49 Videos

Similar Questions

Explore conceptually related problems

If in a triangle ABC,(sin A)/(4)=(sin B)/(5)=(sin C)/(6), the value of cos A+cos B+cos C is equal to

In a triangle ABC, if cos A cos B+sin A sin B sin C=1, then a:b:c is equal to

Knowledge Check

  • If in a triangle ABC,cos A = (sin B)/(2 sin C) , then the triangle is

    A
    equilateral
    B
    isosceles
    C
    right angled
    D
    none of these

  • If in a triangle ABC, cos A sin B= sin C , then the value of tan""A/2 " when " 3b-5c-0 is

    A
    `1/2`
    B
    `3/4`
    C
    `1/sqrt3`
    D
    `0.33`

  • If in a triangle ABC cos Acos B + sin A sin B sin C = 1 , then the triangle is

    A
    isosceles
    B
    right angled
    C
    isosceles right angled
    D
    equilateral

    • Similar Questions

    Explore conceptually related problems

    In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B) , then prove that cos 2A,cos2B and cos 2C are in AP.

    In a triangle ABC,sin A-cos B=cos C then angle B is

    In a triangle ABC, prove b sin B-c sin C=a sin(B-C)

    Statement I If in a triangle ABC sin ^(2) A+sin ^(2)B+sin ^(2)C=2, then one of the angle must be 90^(@). Statement II In any triangles ABC cos 2A+ cos 2B+cos 2C=-1-4 cos A cos B cos C

    In a triangle ABC, sin A -cos B = cos C , then angle B is

    Home
    Profile