[tex]\large\bold{\underline{\underline{To \: Find:-}}}[/tex]
[tex] \sf \left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right|=?[/tex]
[tex]\large\bold{\underline{\underline{Explanation:-}}}[/tex]
They are asking us to find the determinant
[tex]\boxed{\sf \left|\begin{array}{c c} a & b \\ c & d \end{array}\right| =ad-bc}[/tex]
Now using the above formula it becomes
[tex]\left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right| \: = sin20 \degree cos70 \degree - ( - cos20 \degree sin70 \degree) \: \\ \\ = sin20 \degree cos70 \degree + cos20 \degree sin70 \degree [/tex]
Now using the formula
[tex]\boxed{\sf sin(A+B)=sinAcosB+cosAsinB}[/tex]
it becomes
[tex] \longrightarrow \: sin(20 + 70) \\ \\ \longrightarrow \: sin(90 \degree) = 1[/tex]
★Therefore
[tex] \boxed{\sf \left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right|=1}[/tex]
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★Extra information:-
What is a matrix?
☄It is a rectangular representation or array of numbers,symbols and many more functions
☄It is represented in rows and columns
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