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Trigonometrical Equations
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यदि $\left| {\,\begin{array}{*{20}{c}}{\cos (A + B)}&{ - \sin (A + B)}&{\cos 2B}\\{\sin A}&{\cos A}&{\sin B}\\{ - \cos A}&{\sin A}&{\cos B}\end{array}\,} \right| = 0$, तब $B =$
A
$(2n + 1)\frac{\pi }{2}$
B
$n\pi $
C
$(2n + 1)\frac{\pi }{2}$
D
$2n\pi $
Solution
सारणिक का प्रसार करने पर,
${\cos ^2}(A + B) + {\sin ^2}(A + B) + \cos 2B = 0$
$1 + \cos 2B = 0$ या $\cos 2B = \cos \pi $
या $2B = 2n\pi + \pi $ या $B = (2n + 1)\frac{\pi }{2},\,\,n \in Z.$
Standard 11
Mathematics
