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Question

Solve for x if
\(∣ ∣sinxcosxcosxcosxsinxcosxcosxcosxsinx∣ ∣ = 0\\


Solution

∣ ∣sinxcosxcosxcosxsinxcosxcosxcosxsinx∣ ∣=0Applying C1C1+C2+C3∣ ∣sinx+2cosxcosxcosxsinx+2cosxsinxcosxsinx+2cosxsinxsinx∣ ∣=0(2 cosx+sinx)∣ ∣1cosxcosx1sinxcosx1cosxsinx∣ ∣=0ApplyingR2R2R1,R3R3R1(2cosx+sinx)∣ ∣1cosxcosx0sinxcosx000sincosx∣ ∣=0(2cosx+sinx)(sinxcosx)2=02cosx+sinx=0 or sinxcosx=02cosx=sinx or sinx=cosxcot x=12gives no solution inp4xπ4and sinx=cosxtanx=1x=π4.

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