If the two determinants D1 and D2 given below be equal- then prove that cos2- -cos2-cos2-1 where D1- - 1 cos- cos- cos- 1 cos- cos- cos- 1- - - D2- - 0 cos- cos- cos- 0 cos- cos- cos- 0- - -

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Derivative of Standard Functions

If the two de...

Question

If the two determinants $D_{1}$ and $D_{2}$ given below be equal, then prove that
$c o s^{2} θ + c o s^{2} ϕ + c o s^{2} ψ = 1$ where
$D_{1}$ = $∣ ∣ ∣ ∣ \begin{matrix} 1 & c o s θ & c o s ϕ c o s θ & 1 & c o s ψ c o s ϕ & c o s ψ & 1 \end{matrix} ∣ ∣ ∣ ∣$
$D_{2}$ = $∣ ∣ ∣ ∣ \begin{matrix} 0 & c o s θ & c o s ϕ c o s θ & 0 & c o s ψ c o s ϕ & c o s ψ & 0 \end{matrix} ∣ ∣ ∣ ∣$

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D =

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 α + β & α^{2} + β^{2} & 2 α β α + β & 2 α β & α^{2} + β^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

D_{1} =

∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 0 0 & α & β 0 & β & α \end{matrix} ∣ ∣ ∣ ∣

D_{2}

D_{2} = \frac{D}{D_{1}}

d_{1}

d_{2}

d_{1}

d_{2}

(d_{1} > d_{2})

Two holes of unequal diameters $d_{1}$ and $d_{2}$ $(d_{1} > d_{2})$ are cut in a metal sheet. If the sheet is heated

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