Find the value cos A - P cosA- Q cos A - R cosB- P cos B- Q cosB- R cosC - P cosC - Q cos C - R

L.H.S = cos(A P) amp; cos(A Q) amp; cos(A R) cos(B P) amp; cos(B Q) amp; cos(B R) cos(C P) amp; cos(C Q) amp; cos(C R) ...

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Continuity in an Interval

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Find the value $∣ ∣ ∣ ∣ ∣ \begin{matrix} c o s (A - P) & c o s (A - Q) & c o s (A - R) c o s (B - P) & c o s (B - Q) & c o s (B - R) c o s (C - P) & c o s (C - Q) & c o s (C - R) \end{matrix} ∣ ∣ ∣ ∣ ∣$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} c o s (A - P) & c o s (A - Q) & c o s (A - R) c o s (B - P) & c o s (B - Q) & c o s (B - R) c o s (C - P) & c o s (C - Q) & c o s (C - R) \end{matrix} ∣ ∣ ∣ ∣ ∣

A, B, C, P, Q, R ϵ R

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (A + P) & cos (A + Q) & cos (A + R) cos (B + P) & cos (B + Q) & cos (B + R) cos (C + P) & cos (C + Q) & cos (C + R) \end{matrix} ∣ ∣ ∣ ∣ ∣

p, q, r

A, B, C

△ A B C

\frac{1}{p} cos \frac{A}{2} + \frac{1}{q} cos \frac{B}{2} + \frac{1}{r} cos \frac{C}{2}

∣ ∣ ∣ ∣ ∣ \begin{matrix} c o s (A - P) & c o s (A - Q) & c o s (A - R) c o s (B - P) & c o s (B - Q) & c o s (B - R) c o s (C - P) & c o s (C - Q) & c o s (C - R) \end{matrix} ∣ ∣ ∣ ∣ ∣

a, b, c

lim r \to \infty \frac{cos \frac{a}{r} - cos \frac{b}{r} cos \frac{c}{r}}{sin \frac{b}{r} sin \frac{c}{r}}

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