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Prove That: Sin 23° + Sin 37° = Cos 7° - Mathematics

Sum

Prove that:
 sin 23° + sin 37° = cos 7°

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Solution

Consider LHS: 
\[sin 23^\circ + \sin 37^\circ\]
\[ = 2\sin \left( \frac{23^\circ + 37^\circ}{2} \right) \cos \left( \frac{23^\circ - 37^\circ}{2} \right) \left\{ \because \sin A + \sin B = 2sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin 30^\circ \cos \left( - 7^\circ \right)\]
\[ = 2\sin 30^\circ\cos 7^\circ\]
\[ = 2 \times \frac{1}{2}\cos 7^\circ\]
\[ = \cos 7^\circ\]
Hence, LHS = RHS.

Concept: Transformation Formulae
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 8 Transformation formulae
Exercise 8.2 | Q 2.4 | Page 17
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