BeMath-Given-tan-x-y-3-4-tan-x-2-find-tan-y-

Question Number 107932 by bemath last updated on 13/Aug/20

\frac{B e M a t h}{∙}

G i v e n {\begin{cases} \tan (x - y) = \frac{3}{4} \\ \tan x = 2 \end{cases}

f i n d \tan y ?

Commented by mnjuly1970 last updated on 13/Aug/20

e x c e l l e n t .

Commented by mr W last updated on 13/Aug/20

\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y} = \frac{3}{4}

\frac{2 - \tan y}{1 + 2 \tan y} = \frac{3}{4}

10 \tan y = 5

\Rightarrow \tan y = \frac{1}{2}

Commented by bemath last updated on 13/Aug/20

s a n t u y y \dots .

Answered by bemath last updated on 13/Aug/20

\frac{B e M a t h}{° ∙ °}

y = x - (x - y)

\tan y = \tan (x - (x - y))

\tan y = \frac{\tan x - \tan (x - y)}{1 + \tan x \tan (x - y)}

\tan y = \frac{2 - \frac{3}{4}}{1 + 2 (\frac{3}{4})} = \frac{\frac{5}{4}}{\frac{10}{4}} = 0.5

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