1.

If `3 cos theta+4 sin theta=A sin (theta+alpha)`, then values of A and `alpha ` areA. `5,cos ^(-1)((3)/(5))`B. `5, sin^(-1)((3)/(5))`C. `7, sin^(-1)((4)/(5))`D. None of these

Answer» Correct Answer - 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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