Question

Can someone help solve this, thanks.

Let a, β, y be the three interior angles of any triangle, try to prove that cos(a+β+y)= -1.​

Answer 1

Given:

`\alpha, \beta, \gamma` are three interior angles of any triangle.

To prove:

`\cos (\alpha+\beta+\gamma)=-1`

Solution:

Angle sum property of a triangle: According to this theorem the sum of all three interior angle of a triangle is always 180 degrees.

It is given that,
`\alpha, \beta, \gamma` are three interior angles of any triangle.

By using the angle sum property of triangles, we get

`\alpha+\beta+\gamma =180^\circ` ...(i)

We need to prove,

`\cos (\alpha+\beta+\gamma)=-1`

Taking LHS, we get

`LHS=\cos (\alpha+\beta+\gamma)`

`LHS=\cos (180^\circ)` [Using (i)]

`LHS=-1`

`LHS=RHS`

Hence proved.