Question

Вычислите tg49 +tg11/1-tg49*tg11​

Answer 1

Это формула тангенса суммы :

$\frac{tg49^\circ +tg11^\circ }{1-tg49^\circ \cdot tg11^\circ }=tg(49^\circ +11^\circ )=tg60^\circ =\sqrt3$

Answer 2

To compute the value of the expression, we need to use the trigonometric identity:

$\tan(A + B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \cdot \tan(B)}$

In this case, $A = 49^\circ$ and $B = 11^\circ$, so we have:

$\tan(49^\circ + 11^\circ) = \frac{\tan(49^\circ) + \tan(11^\circ)}{1 - \tan(49^\circ) \cdot \tan(11^\circ)}$

Now, let's calculate $\tan(49^\circ)$ and $\tan(11^\circ)$:

$\tan(49^\circ) \approx 1.19175359259$ (rounded to 11 decimal places)

$\tan(11^\circ) \approx 0.19891236738$ (rounded to 11 decimal places)

Now, substitute these values into the formula:

$\frac{\tan(49^\circ) + \tan(11^\circ)}{1 - \tan(49^\circ) \cdot \tan(11^\circ)} = \frac{1.19175359259 + 0.19891236738}{1 - 1.19175359259 \cdot 0.19891236738}$

$\frac{1.39066595997}{0.7648421874} \approx 1.81704572252$

Therefore, the value of the expression is approximately $1.817$ (rounded to three decimal places).