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Transformation Formulae — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTransformation Formulae2 Marks
Question
Prove that: $\sin51^\circ+\cos81^\circ=\cos21^\circ$
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Answer

Consider LHS: $\sin51^\circ+\cos81^\circ$ $=\ \sin51^\circ+\cos(90^\circ-9^\circ)$ $=\ \sin51^\circ+\sin9^\circ$ $=\ 2\sin\Big(\frac{51^\circ+9^\circ}{2}\Big)\cos\Big(\frac{51^\circ-9^\circ}{2}\Big)$ $\Big\{\because\ \sin\text{A}+\sin\text{B}=-2\sin\Big(\frac{\text{A+B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)\Big\}$ $=\ 2\sin30^\circ\cos21^\circ$ $=\ 2\times\frac{1}{2}\cos(21^\circ)$ $=\ \sin(21^\circ)$ $=\ \text{RHS}$ Hence, LHS = RHS.

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