Question

If x and y are acute angles such that sin x=1/√5 and sin y=1/√10 , prove that (x + y) = π/4.

Answer 1

Answer:

Step-by-step explanation:

Taking sin(x+y)=sinxcosy+cosxsinyand substituting the values of sinx,cosx, siny,sinx, we get

sin(x+y)=$(\frac{1}{\sqrt{5}})(\frac{3}{\sqrt{10}})+(\frac{2}{\sqrt{5}})(\frac{1}{\sqrt{10}})$

=$(\frac{1}{\sqrt{2}})(\frac{3}{5})+(\frac{1}{\sqrt{2}})(\frac{2}{5})$

=$\frac{1}{\sqrt{2}}(\frac{3}{5}+\frac{2}{5})$

=$\frac{1}{\sqrt{2}}(1)$

Therefore, sin(x+y)=$\frac{1}{\sqrt{2}}(1)$

⇒$x+y=sin^{-1}(\frac{1}{\sqrt{2}})$

⇒$x+y=\frac{{\pi}}{4}$

Hence proved.