Answer:
Hi there!
As we know that the sum of all three angles of a triangle is 180°.
If ∆ABC is right angled at C
C = 90°
=> [tex]\:\mathsf\red{∠A\: +\:∠B\: +\: ∠C\:=\:180°}[/tex]
=> [tex]\:\sf{∠A\: +\:∠B\: +\: 90°\:=\:180°}[/tex]
=> [tex]\:\sf{∠A\: +\:∠B\: =\:180°\:-\:90°}[/tex]
=> [tex]\:\sf{∠A\: +\:∠B\: =\:90°}[/tex]
Multiplying cos both sides. We get,
=> [tex]\:\sf{cos\:(∠A\: +\:∠B)\: =\:cos\:90°}[/tex]
We know cos 90° = 0, by trigonometric ratio.
=> [tex]\:\sf{cos\:90°\:=\:0}[/tex]
So,
[tex]\:\mathsf{cos(∠A\: +\:∠B)=\:cos\:90°\:=\:0}[/tex]
=> [tex]\:\sf\purple{cos\:(∠A\:+\:∠B)\:=\:0}[/tex]
[tex]\:\mathsf\blue{Hope\:this\:helps\:you!\:}[/tex]
