Question

[tex] \left|\begin{array}{ccc} sin40° -cos40°\\sin50° cos50°\end{array}\right|=...............,Select Proper option from the given options.

(a) 0

(b) 1

(c) -1

(d) not exist [/tex]

Answer 1

HELLO DEAR,

GIVEN:-
LET D = $\left|\begin{array}{cc}sin40&-cos40\\sin50&cos50\end{array}\right|$

using the formula for determinant,

D = |(sin40°)*(cos50°) - (-cos40°)*(sin50°)|

D = |sin40cos50 + cos40sin50|

since, sin(A + B) = sinAcosB + cosAsinB

therefore, D = |sin(40 + 50)|

D = |sin90|

D = 1

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Dear Student,

Answer: Option b (1)

Solution:

Given $\left|\begin{array}{ccc} sin40° -cos40°\\sin50° \:\:cos50°\end{array}\right|$

As we know that if A is a 2 X 2 matrix A ,than Determinant of that $\left|\begin{array}{ccc} a \: \: b\\c \:\:d\end{array}\right|$ = ad-bc

Here a= sin40°
b = -cos40°
c = sin50°
d= cos50°

$\left|\begin{array}{ccc} sin40° -cos40°\\sin50° \:\:cos50°\end{array}\right|$ =

sin 40° cos 50°+ cos 40° sin 50°

As we know that sin A cos B+ cos A sin B= sin (A+B)

So ,

sin 40° cos 50°+ cos 40° sin 50° = sin (40°+50°)

= sin 90°

= 1

So, option B is correct

Hope It helps you.