Question

If x and y are acute such that sin x = 1/√5 and sin y = 1/√10,

prove that

(x + y) = π/4

Answer 1

Given sinx = \(\frac{1}{\sqrt{5}}\) and siny = \(\frac{1}{\sqrt{10}},\)

Now we will calculate value of cos x and cosy

Sin(x + y) = sinx.cosy + cosx.siny

\(\Rightarrow\) sin (x + y) = \(\frac{1}{\sqrt{2}}\)

\(\Rightarrow\) x + y = \(\frac{\pi}{4}\)