Question

Tg(arcsin4/5 + arctg7/24).Sa se calculeze

Answer 1

Salut,

$tg(arcsinx),\;not\breve{a}m\;cu\;u=arcsinx,\;deci\;vrem\;s\breve{a}-l\;afl\breve{a}m\;pe\;tgu;\\\\Din\;u=arcsinx\Rightarrow sinu=x,\;cosu=\sqrt{1-x^2}\Rightarrow tgu=\dfrac{sinu}{cosu}=\dfrac{x}{\sqrt{1-x^2}}.\\\\Deci\;tg(arcsinx)=\dfrac{x}{\sqrt{1-x^2}}\Rightarrow tg\left(arcsin\dfrac{4}5\right)=\dfrac{\dfrac{4}5}{\sqrt{1-\left(\dfrac{4}5\right)^2}}=...=\dfrac{4}3.\\\\\\tg\left[arcsin\left(\dfrac{4}5\right)+arctg\left(\dfrac7{24}\right)\right]=\dfrac{tg\left(arcsin\dfrac{4}5\right)+tg\left(arctg\dfrac7{24}\right)}{1-tg\left(arcsin\dfrac{4}5\right)\cdot tg\left(arctg\dfrac7{24}\right)}=\\\\\\=\dfrac{\dfrac{4}3+\dfrac7{24}}{1-\dfrac{4}3\cdot\dfrac7{24}}=...=\dfrac{117}{44}.$

Green eyes.