Question

If triangleABC is a right angle triangle at C.then what is the value of cos(A+B)

Answer 1

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°

=>
`\:\mathsf\red{∠A\: +\:∠B\: +\: ∠C\:=\:180°}`

=>
`\:\sf{∠A\: +\:∠B\: +\: 90°\:=\:180°}`

=>
`\:\sf{∠A\: +\:∠B\: =\:180°\:-\:90°}`

=>
`\:\sf{∠A\: +\:∠B\: =\:90°}`

Multiplying cos both sides. We get,

=>
`\:\sf{cos\:(∠A\: +\:∠B)\: =\:cos\:90°}`

We know cos 90° = 0, by trigonometric ratio.

=>
`\:\sf{cos\:90°\:=\:0}`

So,

`\:\mathsf{cos(∠A\: +\:∠B)=\:cos\:90°\:=\:0}`

=>
`\:\sf\purple{cos\:(∠A\:+\:∠B)\:=\:0}`

`\:\mathsf\blue{Hope\:this\:helps\:you!\:}`