If ^@\triangle ABC^@ is right angled at ^@C^@, find the value of ^@cos(A+B)^@.



Step by Step Explanation:
  1. We know that sum of the angles of a triangle is ^@180^\circ^@
    ^@\angle A + \angle B + \angle C = 180^\circ^@
  2. It is given that angle ^@C^@ is right angle. Replace ^@\angle C = 90^\circ^@ in above equation
    ^@\implies \angle A + \angle B + 90^\circ = 180^\circ^@
    ^@\implies \angle A + \angle B = 180^\circ - 90^\circ^@
    ^@\implies \angle A + \angle B = 90^\circ^@
  3. Now we know the value of ^@A + B^@, we can find the value of ^@cos(A+B)^@
    ^@\implies cos(A+B) = cos(90^\circ)^@
    ^@\implies cos(A+B) = 0^@

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