Can a wavelet transform give time dependent phase of sinusoids in signal
It is indeed possible (up to a period), with complex "continuous" wavelet transforms, provide your mother wavelet ooscillate sufficiently. You can look at the scalogram modulus and its phase at the appropriate scales, as illustrated from Matlab: Wavelet coherence:



Alternatively, you can convert your signal into an analytic one (using the Hilbert transform) and perform a real wavelet analysis. 

Finally, you might dig into other linear (short-term Fourier transform) or bilinear time-frequency (Wgner-Ville, Choi-Williams) or time-scale tools.