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If (cos A)/3= (cos B)/4= 1/5, - pi/2 lt...

If ` (cos A)/3= (cos B)/4= 1/5, - pi/2 lt A lt 0 and - pi/2 lt B lt 0` then the value of ` 2 sin A + 4 sin B` is

A

4

B

`-2`

C

`-4`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `cos A =3/5 and cos B = 4/5`
` angleA and angleB ` lie on IV quadrant
`sin A = -sqrt(1-9/25) and sinB=-sqrt(1-16/25)`
`Rightarrow sin A = -4/5 and sin B = - 3/5`
Now, ` 2 sin A + 4 sin B = 2(-4/5) +4(-3/5)`
` = - 8/5 - 12/5 = -20/5=-4`
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Knowledge Check

  • If cos A =3/5, cos B=4/5 and (-pi)/(2) lt A lt 0,(-pi)/(2) lt B lt 0, then the value of 2 sin A+4 sin B=

    A
    4
    B
    2
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    0

  • If (cosA)/(3)=(cosB)/(4)=(1)/(5), -pi//2 lt A, B lt 0 , the value of 2sinA+4sinB is equal to

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    4
    B
    2
    C
    `-4`
    D
    0

  • (cosA)/(3)=(cosB)/(4)=(1)/(5), -(pi)/(2) lt A lt 0, 0 lt B lt (pi)/(2) , then 3sinA+4sinB=

    A
    0
    B
    `-1`
    C
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    D
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