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Question
Answer the following questions in one word or one sentence or as per exact requirement of the question.
In a ∆ABC, if sinA and sinB are the roots of the equation \[c^2 x^2 - c\left( a + b \right)x + ab = 0\] then find \[\angle C\]
Solution
It is given that sinA and sinB are the roots of the equation \[c^2 x^2 - c\left( a + b \right)x + ab = 0\]
\[ \Rightarrow \sin A + \sin B = \frac{a + b}{c}\]
\[ \Rightarrow \sin A + \sin B = \frac{k\sin A + k\sin B}{k\sin C} \left( \text{ Sine rule } \right)\]
\[\Rightarrow \sin A + \sin B = \frac{\sin A + \sin B}{\sin C}\]
\[ \Rightarrow \sin C = 1 = \sin90°\]
\[ \Rightarrow C = 90°\]
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