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Question

Find the value ∣ ∣ ∣cos(AP)cos(AQ)cos(AR)cos(BP)cos(BQ)cos(BR)cos(CP)cos(CQ)cos(CR)∣ ∣ ∣

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Solution

L.H.S=∣ ∣ ∣cos(AP)cos(AQ)cos(AR)cos(BP)cos(BQ)cos(BR)cos(CP)cos(CQ)cos(CR)∣ ∣ ∣

=∣ ∣cosAsinA0cosBsinB0cosCsinC0∣ ∣×∣ ∣cosPsinP0cosQsinQ0cosRsinR0∣ ∣(RowbyRow)

=0

=R.H.S


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