Question

answer this question​

Answer 1

To find:

$\sf \left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right|=?$

Explanation:

They are asking us to find the determinant

$\boxed{\sf \left|\begin{array}{c c} a & b \\ c & d \end{array}\right| =ad-bc}$

Now using the above formula it becomes

$\left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right| \: = sin20 \degree cos70 \degree - ( - cos20 \degree sin70 \degree) \: \\ \\ = sin20 \degree cos70 \degree + cos20 \degree sin70 \degree$

Now

using the formula

$\boxed{\sf sin(A+B)=sinAcosB+cosAsinB}$

it becomes

$\longrightarrow \: sin(20 + 70) \\ \\ \longrightarrow \: sin(90 \degree) = 1$

Therefore

$\boxed{\sf \left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right|=1}$

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

Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

To find

$\left[\begin{array}{c c} \sf{sin20} & \sf{-cos20} \\ \sf{sin70} & \sf{cos70} \end{array}\right]$

Thus,

$\implies \: \sf{sin20.cos70 - (- cos20.sin70)}\\ \\ \implies \ \sf{sin20.cos70 + sin70.cos20}$

Of the form,

$\large{\boxed{\sf{sin(A + B) = sinA.cosB + cosA.sinB}}}$

Here,

A = 20° and B = 70°

Implies,

$\implies \sf{sin(20 + 70)} \\ \\ \implies \: \sf{sin90 = 1}$

Thus,the determinant of given matrix is 1