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.

Question

asked Apr 11, 2022 191k views

1 Answer

Stiefel · Answer 1 · 2022-04-18T03:27:13+0000

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.