નિશ્ચાયક left| begin{array}{ccc} 1 & cos(alph | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) ધારો કે $D = \left| \begin{array}{ccc} 1 & \cos(\alpha - \beta) & \cos \alpha \ \cos(\alpha - \beta) & 1 & \cos \beta \ \cos \alpha & \cos \beta

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) ધારો કે $D = \left| \begin{array}{ccc} 1 & \cos(\alpha - \beta) & \cos \alpha \ \cos(\alpha - \beta) & 1 & \cos \beta \ \cos \alpha & \cos \beta & 1 \end{array} ight|$.પ્રથમ હાર મુજબ વિસ્તરણ કરતા:$D = 1(1 - \cos^2 \beta) - \cos(\alpha - \beta)(\cos(\alpha - \beta) - \cos \alpha \cos \beta) + \cos \alpha(\cos \beta \cos(\alpha - \beta) - \cos \alpha)$.નિત્યસમ $\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$ નો ઉપયોગ કરતા:$D = \sin^2 \beta - \cos(\alpha - \beta)(\sin \alpha \sin \beta) + \cos \alpha(\cos \beta(\cos \alpha \cos \beta + \sin \alpha \sin \beta) - \cos \alpha)$.$D = \sin^2 \beta - \cos(\alpha - \beta)\sin \alpha \sin \beta + \cos \alpha(\cos \alpha \cos^2 \beta + \sin \alpha \sin \beta \cos \beta - \cos \alpha)$.$D = \sin^2 \beta - \cos(\alpha - \beta)\sin \alpha \sin \beta + \cos^2 \alpha \cos^2 \beta + \sin \alpha \sin \beta \cos \alpha \cos \beta - \cos^2 \alpha$.$D = \sin^2 \beta - \cos(\alpha - \beta)\sin \alpha \sin \beta + \cos^2 \alpha(\cos^2 \beta - 1) + \sin \alpha \sin \beta \cos \alpha \cos \beta$.$D = \sin^2 \beta - \sin \alpha \sin \beta(\cos(\alpha - \beta) - \cos \alpha \cos \beta) - \cos^2 \alpha \sin^2 \beta$.$D = \sin^2 \beta - \sin \alpha \sin \beta(\sin \alpha \sin \beta) - \cos^2 \alpha \sin^2 \beta$.$D = \sin^2 \beta - \sin^2 \alpha \sin^2 \beta - \cos^2 \alpha \sin^2 \beta$.$D = \sin^2 \beta - \sin^2 \beta(\sin^2 \alpha + \cos^2 \alpha) = \sin^2 \beta - \sin^2 \beta(1) = 0$.

નિશ્ચાયક $\left| \begin{array}{ccc} 1 & \cos(\alpha - \beta) & \cos \alpha \\ \cos(\alpha - \beta) & 1 & \cos \beta \\ \cos \alpha & \cos \beta & 1 \end{array} \right|$ નું મૂલ્ય છે

Similar Questions

જો બિંદુઓ $A, B,$ અને $C$ ના યામ અનુક્રમે $(4, 4), (3, -2),$ અને $(3, -16)$ હોય,તો ત્રિકોણ $ABC$ નું ક્ષેત્રફળ શોધો.

ઉગમબિંદુ $(0, 0)$ ને બિંદુ $(-4, 5)$ સાથે જોડતી રેખાનું સમીકરણ શું છે?

$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|=$

જો $\omega$ એ એકમનું સંકર ઘનમૂળ હોય,તો નિશ્ચાયક $\left| \begin{array}{ccc} 2 & 2\omega & -\omega^2 \\ 1 & 1 & 1 \\ 1 & -1 & 0 \end{array} \right|$ નું મૂલ્ય શોધો.

Vedclass Test Series

Exam Paper Generator

Online Exam Module