Cos(2x-5°)-sin(2x-5°)=((Sqrt(2))/(2))

Cos(2x-5°)-sin(2x-5°)=((Sqrt(2))/(2))

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  1. Đáp án:

    \(\left[ \matrix{
    x = {10^0} + k{180^0} \hfill \cr
    x = – {50^0} + k{180^0} \hfill \cr} \right.\,\,\left( {k \in Z} \right)\)

    Giải thích các bước giải:

    $$\eqalign{
    & \cos \left( {2x – {5^0}} \right) – \sin \left( {2x – {5^0}} \right) = {{\sqrt 2 } \over 2} \cr
    & \Leftrightarrow {1 \over {\sqrt 2 }}\cos \left( {2x – {5^0}} \right) – \sin \left( {2x – {5^0}} \right) = {1 \over 2} \cr
    & \Leftrightarrow \cos \left( {2x – {5^0}} \right)\cos {45^0} – \sin \left( {2x – {5^0}} \right)\sin {45^0} = {1 \over 2} \cr
    & \Leftrightarrow \cos \left( {2x – {5^0} + {{45}^0}} \right) = {1 \over 2} \cr
    & \Leftrightarrow \cos \left( {2x + {{40}^0}} \right) = {1 \over 2} \cr
    & \Leftrightarrow \left[ \matrix{
    2x + {40^0} = {60^0} + k{360^0} \hfill \cr
    2x + {40^0} = – {60^0} + k{360^0} \hfill \cr} \right. \cr
    & \Leftrightarrow \left[ \matrix{
    2x = {20^0} + k{360^0} \hfill \cr
    2x = – {100^0} + k{360^0} \hfill \cr} \right. \cr
    & \Leftrightarrow \left[ \matrix{
    x = {10^0} + k{180^0} \hfill \cr
    x = – {50^0} + k{180^0} \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr} $$

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