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If 3 cos theta+4 sin theta=A sin (theta+...

If `3 cos theta+4 sin theta=A sin (theta+alpha)`, then values of A and `alpha ` are

A

`5,cos ^(-1)((3)/(5))`

B

`5, sin^(-1)((3)/(5))`

C

`7, sin^(-1)((4)/(5))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`3costheta+4sin theta=5[(3)/(5)cos theta+(4)/(5)sin theta]`
`=5[ sin alpha cos theta + cos alpha sin theta]=5 sin (theta+alpha)`
Therefore A=5 and `alpha=sin^(-1)((3)/(5))`
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