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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:
2
`3costheta + 4sintheta = 5[(3)/(5)cos theta + (4)/(5) sin theta]`
`= 5[ sin alpha cos theta + cosalpha sintheta] = 5sin (theta + alpha)`
Therefore `A=5 and alpha = sin^(-1)((3)/(5))`
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