The determinant \( \left|\begin{array}{lll}\sin ^{2} \alpha & \sin ...
The determinant \( \left|\begin{array}{lll}\sin ^{2} \alpha & \sin \alpha \cos \alpha & \cos ^{2} \alpha \\ \sin ^{2} \beta & \sin \beta \cos \beta & \cos ^{2} \beta \\ \sin ^{2} \gamma & \sin \gamma \cos \gamma & \cos ^{2} \gamma\end{array}\right| \) is
(a) \( -\sin (\beta-\gamma) \sin (\gamma-\alpha) \sin (\alpha-\beta) \)
(b) \( \sin (\alpha-\beta) \cos \alpha \cos \beta \)
\( +\sin (\beta-\gamma) \cos \beta \cos \gamma \)
\( +\sin (\gamma-\alpha) \cos \gamma \cos \alpha \)
(c) \( \frac{1}{4}[\sin (2 \alpha-2 \beta)+\sin (2 \beta-2 \gamma)+ \)
\( \sin (2 \gamma-2 \alpha)] \)
(d) none of these.
π² PW App Link - https://bit.ly/YTAI_PWAP
π PW Website - https://www.pw.live/
Other Videos By PW Solutions
| 2023-02-25 | A set of vector \( \left\{\left(a_{1}, a_{2}, a_{3}\right),\left(b_... |
| 2023-02-25 | A set of vector \( \left\{\left(a_{1}, a_{2}, a_{3}\right),\left(b_... |
| 2023-02-25 | Each question in this section has four choices (a), (b), (c) and (d... |
| 2023-02-25 | Each question in this section has four choices (a), (b), (c) and (d... |
| 2023-02-25 | A set of vector \( \left\{\left(a_{1}, a_{2}, a_{3}\right),\left(b_... |
| 2023-02-25 | A set of vector \( \left\{\left(a_{1}, a_{2}, a_{3}\right),\left(b_... |
| 2023-02-25 | Factors of
\( \Delta=\left|\begin{array}{ccc}x^{3} & y^{3} & z^{3} ... |
| 2023-02-25 | Each question in this section has four choices (a), (b), (c) and (d... |
| 2023-02-25 | Let \( A, B \) and \( C \) be \( 2 \times 2 \) matrices with entrie... |
| 2023-02-25 | Each question in this section has four choices (a), (b), (c) and (d... |
| 2023-02-25 | The determinant \( \left|\begin{array}{lll}\sin ^{2} \alpha & \sin ... |
| 2023-02-25 | If \( \Delta=\left|\begin{array}{ccc}\cos \alpha & \sin \alpha \cos... |
| 2023-02-25 | If \( a, b, c \in \boldsymbol{R} \) and \( a^{2}+b^{2}-a b-a-b+1 \l... |
| 2023-02-25 | If \( a_{i}, b_{i} \in \mathbf{N} \) for \( i=1,2,3 \) then the coe... |
| 2023-02-25 | If \( \phi \in \mathbf{R} \) then \( \Delta(\phi)= \)
\[
\left|\beg... |
| 2023-02-25 | If \( a b c \neq 0 \), then
\[
\Delta(x)=\left|\begin{array}{ccc}
a... |
| 2023-02-25 | If \( \Delta=\left|\begin{array}{ccc}\sin \alpha & \cos \alpha & \s... |
| 2023-02-25 | If \( a^{2}+b^{2}+c^{2}=1 \), then
\[
\left|\begin{array}{cc}
a^{2}... |
| 2023-02-25 | If \( a_{i}, b_{i}, c_{i} \in \mathbf{R}(i=1,2,3) \) and \( x \in \... |
| 2023-02-25 | Let \( a, b, c, d \) be four real numbers and let
\[
\Delta=\left|\... |
| 2023-02-25 | If \( a \neq b \), the equation \( \left|\begin{array}{ccc}x & a & ... |
0