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Papessa [141]
3 years ago
13

Can someone help solve this, thanks.

Mathematics
1 answer:
qwelly [4]3 years ago
6 0

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.

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