Question

if sinX*cosY=1/4and 3tanX=4tanY then sin(X-Y)=

Answer 1

Answer on Question #49553 – Math – Trigonometry

Task:

if sinX*cosY=1/4 and 3tanX=4tanY then sin(X-Y)=

Solution:

$$\sin x \cos y = \frac{1}{4}$$ $$3 \tan x = 4 \tan y$$ $$3 \frac{\sin x}{\cos x} = 4 \frac{\sin y}{\cos y} \Rightarrow 3 \sin x \cos y = 4 \sin y \cos x, \sin x \cos y = \frac{1}{4} \Rightarrow \frac{3}{4} = 4 \sin y \cos x \Rightarrow \sin y \cos x = \frac{3}{16}$$ $$\sin(x - y) = \sin x \cos y - \cos x \sin y = \frac{1}{4} - \frac{3}{16} = \frac{1}{16}$$

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