TS EAMCET 20-July-2022 Shift 1 Solved Paper

For x∈[0,2π]
sin‌x+i⋅cos‌2‌x and cos‌x−isin‌2x are conjugate to each other.
⇒sin‌x+i‌cos‌2‌x=cos‌x−isin‌2x
sin‌x+i‌cos‌2‌x=cos‌x+isin‌2x....(i)
On comparing both side of Eq. (i), we get
sin‌x=cos‌x‌‌;‌‌sin‌2x=cos‌2‌x
⇒‌‌x=‌

π

4

,‌

5π

4

‌‌;‌‌tan‌2‌x=1
But there is no common value of x which satisfy both the condition. So, x=φBut there is no common value of x which satisfy both the condition. So, x=φ