\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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2 Answers
106sint+ 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
