value of m

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\hspace{-16}$Find value of $\mathbf{m}$ in \\\\ $\mathbf{\begin{Vmatrix} 50\sin^2 t+5m\sin t+(4m-41)=0 \\\\ 50\cos^2 t+5m\cos t+(4m-41)=0 & \end{Vmatrix}}$\\\\\\ and $\mathbf{\tan t\neq o}.$ Then value of $\mathbf{m}$ is

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Asish Mahapatra ·2011-11-08 01:17:53

sint+ cost = 32-8m5m (adding both equations and rearranging)

(50(cost+sint) + 5m)(cost-sint)=0 (subtracting both equations)

=> sint + cost = -m/10 OR tant = 1

Equating the bolded parts

=> -m10 = 32-8m5m

=> -5m² = 320 - 80m
=> m² - 16m + 64 = 0
=> (m-8)² = 0
=> m=8

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1708

man111 singh ·2011-11-14 11:04:58

thanks ashish

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° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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value of m

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