For all the values of A-B-C and P-Q-R- the value of 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 is-

We have, cos (A P) amp;cos (A Q) nbsp; amp;cos (A R) nbsp; cos (B P) amp;cos (B Q) nbsp; amp;cos (B R) nbsp; cos (C P) amp;cos (C Q) ...

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Equality of Matrices

For all the v...

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For all the values of $A, B, C$ and $P, Q, R$ , the value of $∣ ∣ ∣ ∣ ∣ \begin{matrix} cos (A - P) & cos (A - Q) & cos (A - R) cos (B - P) & cos (B - Q) & cos (B - R) cos (C - P) & cos (C - Q) & cos (C - R) \end{matrix} ∣ ∣ ∣ ∣ ∣$ is:

1

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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} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ ∣ \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} ∣ ∣ ∣ ∣ ∣

a, b

c

△ A B C

a^{2}, b^{2}, c^{2}

x^{3} - P x^{2} + Q x - R = 0

P, Q, R

\frac{cos A}{A} + \frac{cos B}{B} + \frac{cos C}{C}

P, Q

R

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