Question

if sin alpha is equal to 1 by root 2 and 10 beta is equal to 1 then find sin alpha + beta where alpha and beta are acute angles

Answer 1

Dear student
$$\begin{gathered} \mathrm{Assuming}\mathrm{your}\mathrm{question}\mathrm{as} \\ \mathrm{If}\mathrm{sin\alpha }=\frac{1}{\sqrt{2}}\mathrm{and}\mathrm{tan\beta }=1,\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\sin \left(\mathrm{\alpha }+\mathrm{\beta }\right)\mathrm{where}\mathrm{\alpha }\mathrm{and}\mathrm{\beta }\mathrm{are}\mathrm{acute}\mathrm{angles}. \\ \mathrm{Solution}:\mathrm{sin\alpha }=\frac{1}{\sqrt{2}} \\ \Rightarrow \mathrm{sin\alpha }=\sin \left(45°\right) \\ \Rightarrow \mathrm{\alpha }=45° \\ \mathrm{and}\mathrm{tan\beta }=1 \\ \Rightarrow \mathrm{tan\beta }=\tan (45°) \\ \Rightarrow \mathrm{\beta }=45° \\ \mathrm{So},\mathrm{\alpha }+\mathrm{\beta }=45°+45°=90° \\ \mathrm{hence}\sin \left(\mathrm{\alpha }+\mathrm{\beta }\right)=\sin 90°=1 \end{gathered}$$
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