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Transformation Formulae — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTransformation Formulae2 Marks
Question
Prove that: $\cos100^\circ+\cos20^\circ=\cos40^\circ$
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Answer

$\cos100^\circ+\cos20^\circ=\cos40^\circ$ $\text{LHS}=\cos100^\circ+\cos20^\circ$ $[\because\ \cos\text{C}+\cos\text{D}=2\cos\frac{\text{C+D}}{2}\cos\frac{\text{C}-\text{D}}{2}]$ $\Rightarrow\ 2\cos\frac{(100^\circ+20^\circ)}{2}\cos\frac{100^\circ-20^\circ}{2}$ $=\ 2\cos60^\circ\cos40^\circ$ $=\ 2\times\frac{1}{2}\cos40^\circ$ $\Big[\because\ \cos60^\circ=\frac{1}{2}\Big]$ $=\ \cos40^\circ=\text{RHS}$

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