Left|begin{array}{ccc}cos α cos β & cos α operatorname{csin} β & -sin α -sin β & c

English

Gujarati

Hindi

3 and 4 .Determinants and Matrices

hard

$\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \operatorname{csin} \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$ નું મૂલ્ય શોધો.

$2$

$-1$

$1$

$0$

Solution

$\Delta=\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \operatorname{csin} \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$

Expanding along $C_{3},$ we have:

$\Delta=-\sin \alpha\left(-\sin \alpha \sin ^{2} \beta+\cos ^{2} \beta \sin a\right)+\cos \alpha\left(\cos \alpha \cos ^{2} \beta+\cos \alpha \sin ^{2} \beta\right)$

$=\sin ^{2} \alpha\left(\sin ^{2} \beta+\cos ^{2} \beta\right)+\cos ^{2} \alpha\left(\cos ^{2} \beta+\sin ^{2} \beta\right)$

$=\sin ^{2} \alpha(1)+\cos ^{2} \alpha(1)$

$=1$

Standard 12

Mathematics

$\left| {\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\sin }^2}\theta }&{{{\sin }^2}\theta }\\{{{\cos }^2}\theta }&{1 + {{\cos }^2}\theta }&{{{\cos }^2}\theta }\\{4\sin 4\theta }&{4\sin 4\theta }&{1 + 4\sin 4\theta }\end{array}} \right| = 0$ તો $\sin\, 4\theta $ મેળવો.

hard

શૂન્યતર $a$ માટે સમીકરણ $\left| {\begin{array}{*{20}{c}}
{x + a}&x&x\\
x&{x + a}&x\\
x&x&{x + a}
\end{array}} \right| = $ ઉકેલો.

medium

જો $\left| {\,\begin{array}{*{20}{c}}{x + 1}&{x + 2}&{x + 3}\\{x + 2}&{x + 3}&{x + 4}\\{x + a}&{x + b}&{x + c}\end{array}\,} \right| = 0$, તો $a,b,c$ એ . . . શ્રેણીમાં છે.

medium

$\Delta=\left|\begin{array}{lll}1 & a & b c \\ 1 & b & c a \\ 1 & c & a b\end{array}\right|$ નું મૂલ્ય શોધો.

medium

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\{b + c}&{c + a}&{a + b}\\{b + c – a}&{c + a – b}&{a + b – c}\end{array}\,} \right|$ = . .

easy

$\left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \operatorname{csin} \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right|$ નું મૂલ્ય શોધો.

Solution

Similar Questions

$\left| {\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\sin }^2}\theta }&{{{\sin }^2}\theta }\\{{{\cos }^2}\theta }&{1 + {{\cos }^2}\theta }&{{{\cos }^2}\theta }\\{4\sin 4\theta }&{4\sin 4\theta }&{1 + 4\sin 4\theta }\end{array}} \right| = 0$ તો $\sin\, 4\theta $ મેળવો.

શૂન્યતર $a$ માટે સમીકરણ $\left| {\begin{array}{*{20}{c}} {x + a}&x&x\\ x&{x + a}&x\\ x&x&{x + a} \end{array}} \right| = $ ઉકેલો.

જો $\left| {\,\begin{array}{*{20}{c}}{x + 1}&{x + 2}&{x + 3}\\{x + 2}&{x + 3}&{x + 4}\\{x + a}&{x + b}&{x + c}\end{array}\,} \right| = 0$, તો $a,b,c$ એ . . . શ્રેણીમાં છે.

$\Delta=\left|\begin{array}{lll}1 & a & b c \\ 1 & b & c a \\ 1 & c & a b\end{array}\right|$ નું મૂલ્ય શોધો.

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\{b + c}&{c + a}&{a + b}\\{b + c – a}&{c + a – b}&{a + b – c}\end{array}\,} \right|$ = . .

Start a Free Trial Now

શૂન્યતર $a$ માટે સમીકરણ $\left| {\begin{array}{*{20}{c}}
{x + a}&x&x\\
x&{x + a}&x\\
x&x&{x + a}
\end{array}} \right| = $ ઉકેલો.