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In triangle ABC, if cosA+sinA-(2)/(cosB+...

In `triangle ABC`, if `cosA+sinA-(2)/(cosB+sinB)=0` then prove that triangle is isosceles right angled.

Text Solution

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Given `(cosA+sinA)(cosB+sinB)=2`
`rArrcos(A-B)+sin(A+B)=2`
`rArr cos(A-B)=1,sin(A+B)=1`
`rArr A=B,A+B=(pi)/(2)`
`rArr C=(pi)/(2)`
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