sinx + i cos 2x and cos x - i sin2x are conjugate to each other for(A) x=nπ (B) x=(n+1/2)π/2 (C) x=0 (D) no value of xA. `x = npi`B. `x = ("n" +(1)/(2))(pi)/(2)`C. x=0D. No value of x

sinx + i cos 2x and cos x - i sin2x are conjugate to each other for(A)

1.	sinx + i cos 2x and cos x - i sin2x are conjugate to each other for(A) x=nπ (B) x=(n+1/2)π/2 (C) x=0 (D) no value of xA. `x = npi`B. `x = ("n" +(1)/(2))(pi)/(2)`C. x=0D. No value of x
Answer» Correct Answer - D let `z= sinx +icos2x ` and `barz = sinx - 2x " "...(i)` Given that, `barz = cosx - isin 2x" "...(ii)` `:. sinx - icon 2x = cos x - isin 2x` `rArr sin x = cos x and cos2x = sin2 x ` `rArr tanx = 1 "and" 2x =1 ` `rArr tan x = "tan"(pi)/(4) "and" 2x = "tan"(pi)/(4)` `rArr x =npi + (pi)/(4) "and" 2x = 2pi + (pi)/(4) ` `rArr 2x - x = 0 rArr x = 0 `