Question

If $sinxcosy=\frac{1}{4}$ and $3tanx=4tany$, then $sin(x+y)$ is equal to

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. 1
• D. none of these

Answer 1

The correct option is D none of these

$sinxcosy=\frac{1}{4}$ ...(1)

$3tanx=4tany\Rightarrow 3sinxcosy=4sinxcosy$

From (1) we get

$\frac{3}{4}=4sinxcosy\Rightarrow sinxcosy=\frac{3}{16}$ ...(2)

Therefore from (1) and (2) we get

$sin(x+y)=sinxcosy+cosxsiny=\frac{1}{4}+\frac{3}{16}=\frac{7}{16}$