If = 0 then B =

Engineering

Mathematics

Introduction to Determinants

Question

If $∣ \begin{array}{ccc} \cos (A + B) & - \sin (A + B) & \cos 2 B \\ sinA & cosA & sinB \\ - cosA & sinA & cosB \end{array} ∣$ = 0 then B =

(2n + 1) $\frac{π}{2}$

nπ

(2n + 1)π

2n π

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⇒ cos⁡(A + B)(cos⁡A cos⁡B – sin⁡A sin⁡B) + sin²⁡(A + B) + cos⁡2B + 0

⇒ cos²⁡(A + B) + sin²⁡(A + B) + cos⁡2B = 0

⇒ cos⁡(2B) = – 1

2B = (2n + 1)π

B = (2n + 1)π/2

so (2n + 1)π/2

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