Question

if tan ^-1 (1/2) + tan^-1 (2/11) = tan ^-1 a. Then a is​

Answer 1

Answer:

,99 because 6+aa is 99 :::

Answer 2

Question

$\sf{tan ^{-1} \: \dfrac{1}{2}+ tan^{-1} \: \dfrac{2}{11}= tan ^{-1}a.}$

Topic -

• Inverse trigonometry

Formula used -

$\sf{ \bull \: tan^{-1} x+ tan^{ - 1}y= tan^{-1} \: \dfrac{x+y}{1-(x×y)}}$

Solution

Using the formula first we will solve the L.H.S so,

$\sf{\implies tan^{-1} \: \dfrac{1}{2}+ tan^{-1} \: \dfrac{2}{11}= tan^{-1} \: \dfrac{\frac{1}{2}+\frac{2}{11} }{1- \bigg(\frac{1}{2}×\frac{2}{11} \bigg)}}$

$\sf{\implies \: \: tan^{-1} \: \: \dfrac{ \frac{11 + 4}{22}}{1 - \frac{2}{22}}}$

$\sf{\implies \: \: tan^{-1} \: \: \dfrac{ \frac{15}{22}}{ \frac{22 - 2}{22} } }$

$\sf{\implies \: \: {tan^{-1} \: \: \frac{15}{20} }} \\ \\ \sf{\implies \red{ tan^{-1} \: \dfrac{3}{4} }}$

$\sf{ \to \: R.H.S \: is \: given \: as \: tan^{-1} a}$

$\sf{ \implies \: tan^{-1} a = tan^{-1} \: \dfrac{3}{4} } \\ \\ \bold{ \implies \: \green{a = \frac{3}{4} }}$

⭐ so the value of a is 3/4

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