The maximum value of Δ $$=$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$+$$ $$sin$$θ $$11+$$$$cos$$θ $$1$$ $$1$$ is (where$$ , θ is real $$number)

Question

The maximum value of Δ $$=$$ $$1$$                  $$1$$           $$1$$ $$1$$            $$1$$ $$+$$ $$sin$$θ     $$11+$$$$cos$$θ      $$1$$           $$1$$  is (where$$ , θ is real $$number)

Infinity Learn · Accepted Answer

Δ $$=$$ $$1$$                  $$1$$           $$1$$ $$1$$            $$1$$ $$+$$ $$sin$$θ     $$11+$$$$cos$$θ      $$1$$           $$1$$ $$=$$ $$0$$            $$0$$           $$1$$ $$0$$           $$sin$$ θ       $$1cos$$ θ      $$0$$           $$1$$                                                     ∵$$C1$$→$$C1$$−$$C3$$ and $$C2$$→$$C2-C3=-($$$$sin$$θ·$$cos$$θ$$)=-12$$·$$2sin$$θ$$cos$$θ$$=-12sin2$$θSince the maximum value of $$sin2$$θis $$1$$. So far maximum value of θ   should be $$-45$$°.Δ$$=-12sin2$$.$$-45$$°$$=-12sin-90$$°$$=12$$·$$1=12$$

Introduction to Determinants

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The maximum value of $Δ = |\begin{array}{l} 1 1 1 \\ 1 1 + sin θ 1 \\ 1 + \cos θ 1 1 \end{array}|$ $is (where, θ is real number)$

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Introduction to Determinants

Remember concepts with our Masterclasses.

The maximum value of Δ = 1 1 1 1 1 + sinθ 11+cosθ 1 1 is (where , θ is real number)

Δ = 1 1 1 1 1 + sinθ 11+cosθ 1 1 = 0 0 1 0 sin θ 1cos θ 0 1 ∵C1→C1−C3 and C2→C2-C3=-(sinθ·cosθ)=-12·2sinθcosθ=-12sin2θSince the maximum value of sin2θis 1. So far maximum value of θ should be -45°.Δ=-12sin2.-45°=-12sin-90°=12·1=12

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The maximum value of $Δ = |\begin{array}{l} 1 1 1 \\ 1 1 + sin θ 1 \\ 1 + \cos θ 1 1 \end{array}|$ $is (where, θ is real number)$