If `DeltaABC` is right angled at `C`, then the value of `cos(A+B)` is

Options

A. 0
B. 1
C. `1/2`
D. `sqrt(3)/2`

Answer

A

Explanation

We know that, in `DeltaABC`, sum of three angles =`180^(@)`
i.e., `angleA + angleB + angleC=180^(@)`
But right angled at C i.e., `angleC=90^(@)` (given)
`angleA + angleB + 90^(@)=180^(@)`
`rArr A+B=90^(@)` `[therefore angleA=A]`
`therefore` cos(A+B)`=cos90^(@)=0`