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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 - Mathematics

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 \[\angle C\]  

 

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Solution

It is given that sinA and sinB are the roots of the equation \[c^2 x^2 - c\left( a + b \right)x + ab = 0\] 

\[\therefore \sin A + \sin B = - \frac{- c\left( a + b \right)}{c^2} \left( \text{ Sum of roots } = - \frac{b}{a} \right)\]
\[ \Rightarrow \sin A + \sin B = \frac{a + b}{c}\]
\[ \Rightarrow \sin A + \sin B = \frac{k\sin A + k\sin B}{k\sin C} \left( \text{ Sine rule } \right)\] 

\[\Rightarrow \sin A + \sin B = \frac{\sin A + \sin B}{\sin C}\]
\[ \Rightarrow \sin C = 1 = \sin90°\]
\[ \Rightarrow C = 90°\] 

Concept: Sine and Cosine Formulae and Their Applications
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 10 Sine and cosine formulae and their applications
Q 5 | Page 26
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