Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If Cot (α + β) = 0, Then Write the Value of Sin (α + 2β). - Mathematics

If cot (α + β) = 0, then write the value of sin (α + 2β).

 
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Solution

\[\cot \left( \alpha + \beta \right) = 0\]
\[ \Rightarrow \alpha + \beta = \frac{\pi}{2} \left( 1 \right)\]
\[\beta = \frac{\pi}{2} - \alpha \left( 2 \right)\]
\[\alpha = \frac{\pi}{2} - \beta \left( 3 \right)\]
\[\text{ Now, }\sin\left( \alpha + 2\beta \right) = \sin\left( \alpha + \beta + \beta \right)\]
\[ = \sin\left( \frac{\pi}{2} + \frac{\pi}{2} - \alpha \right)\]
\[ = \sin\left( \pi - \alpha \right)\]
\[ = \sin \alpha\]
\[\text{ Now, }\sin\left( \alpha + 2\beta \right) = \sin\left( \alpha + 2\beta \right)\]
\[ = \sin\left( \frac{\pi}{2} - \beta + 2\beta \right)\]
\[ = \sin\left( \frac{\pi}{2} + \beta \right)\]
\[ = \cos \beta\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 5 Trigonometric Functions
Q 13 | Page 41
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