Trigonometrical Equations
medium

જો $\left| {\,\begin{array}{*{20}{c}}{\cos (A + B)}&{ - \sin (A + B)}&{\cos 2B}\\{\sin A}&{\cos A}&{\sin B}\\{ - \cos A}&{\sin A}&{\cos B}\end{array}\,} \right| = 0$ તો $B =$

A

$(2n + 1)\frac{\pi }{2}$

B

$n\pi $

C

$(2n + 1)\frac{\pi }{2}$

D

$2n\pi $

Solution

(a) On expanding determinant,

${\cos ^2}(A + B) + {\sin ^2}(A + B) + \cos 2B = 0$

$1 + \cos 2B = 0$ or $\cos 2B = \cos \pi $

or $2B = 2n\pi + \pi $ or $B = (2n + 1)\frac{\pi }{2},\,\,n \in Z.$

Standard 11
Mathematics

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