Two waves represented by y= a sin(wt - kx) and y= a cos(wt - kx) are superposed The resultant wave will have an amplitude?

Dear Student,
Please find below the solution to your problem.

Given, y1 ​= asin(ωt-kx)
y2 ​= acos(ωt-kx)
or y2​ = asin(ωt-kx+2π​)
Phase difference of two waves = 2π​
∵ Resultant amplitude
R = a2 + a2 + 2aacosϕ​
= a2 + a2 + 2a2^cos2π​​
= 2a^2​ (∵cos2π​=0)
R = 2​a.y1
= asin⁡(ωt-kx)

Thanks and Regards