In a triangle - ABC prove that sin A-sin Bsin C-

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Standard XII

Mathematics

Sine Rule

In a triangle...

Question

In a triangle $Δ A B C$ prove that $sin A + sin B > sin C$ .

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Solution

Let $a, b, c$ be the sides of the triangle $Δ A B C$ .
Now the construction of the triangle is possible if sum of any two sides is greater than the other.
Then we shall get,
$a + b > c$
or, $2 R sin A + 2 R sin B > 2 R sin C$ [ Using sine rule of triangle]
or, $sin A + sin B > sin C$ . [ Since $R$ is circum-radius of the triangle $Δ A B C$ , so $R > 0$ ]

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In a triangle ΔABC prove that sinA+sinB>sinC.

In a triangle $Δ A B C$ prove that $sin A + sin B > sin C$ .