two sinusoidal waves traveling in the same direction having same frequency but different amplitudes and maintaining a phase difference derive an expression for intensity of maxima and minima.

Answer 1

the waves are

a sin(x) and b sin(x-k)

add them up and you have

a sinx + b(sinx cosk - cosx sink)
= (a+b*cosk)sinx - (b*sink)cosx

This is basically just
Asinx + Bcosx
which can be reduced to a single sine wave of amplitude √(A^2+B^2)

See a nice discussion at

https://en.wikibooks.org/wiki/Trigonometry/Simplifying_a_sin(x)_%2B_b_cos(x)