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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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Knowledge Check

  • In triangleABC , if cosA=sinB-cosC , then the triangle is

    A
    a right angled
    B
    an isosceles
    C
    an equilateral
    D
    a scalene

  • In triangle ABC, 2(bc cosA-ac cosB-ab cosC)=

    A
    `0`
    B
    `(a+b+c)`
    C
    `-3a^(2)+b^(2)+c^(2)`
    D
    `2(a^(2)+b^(2)+c^(2))`

  • If in triangle ABC, cosA=(sinB)/(2sinC) , then the triangle is

    A
    Equilateral
    B
    Isosceles
    C
    Right angled
    D
    Obtuse triangle

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