sin(α+1∘)+cos(β+1∘)=2{21⋅sin(α+1∘)+21⋅cos(β+1∘)}=2{cos45∘⋅sin(α+1)+sin45∘⋅cos(α+1)}(∵α=β)$\begin{aligned}
& =\sqrt{2}\left\{\sin \left(\alpha+1+45^{{}^{\circ}}\right)\right\}=\sqrt{2} \cdot \sin \left(15^{{}^{\circ}}+1^{{}^{\circ}}+45^{{}^{\circ}}\right) \\
& =\sqrt{2} \cdot \sin 61^{{}^{\circ}} (i)
\end{aligned}
Again
21(3⋅cos1∘+sin1∘)=22(23⋅cos1∘+21sin1∘)=2⋅(sin60∘⋅cos1∘+cos60∘⋅sin1∘)=2(sin61∘)(ii) Thus ( i )=( ii )\frac{1}{\sqrt{2}} \left(\sqrt{3} \cdot \cos1^{{}^{\circ}}+\sin 1^{{}^{\circ}}\right)$.
