If ∆ABC is right angled at C, then the value of cos (A + B) is ______.

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KollegeApply · Accepted Answer

If ∆ABC is right angled at C, then the value of cos (A + B) is 0. Explanation: We know that, In ∆ABC, Sum of three angles = $180^\circ$ i.e., $\angle$A + $\angle$B + $\angle$C = $180^\circ$ But right angled at C i.e., $\angle$C = $90^\circ$ ...[Given] $\angle$A + $\angle$B + $90^\circ$ = $180^\circ$ $\Rightarrow$ A + B = $90^\circ$ ...[∵$\angle$A = A] $\therefore$ cos (A + B) = cos $90^\circ$ = 0 [Solution diagram: 63360_solution_1.png]

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