Question

Tan inverse x upon 2 + 10 inverse x upon 3 is equal to 5 by 4 find the value of x

Answer 1

Answer: The value of x = 0.0259.

Step-by-step explanation:

Since we have given that

$\tan^{-1}\frac{x}{2}+\tan^{-1}\frac{x}{3}=\frac{5}{4}$

As we know the formula for :

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

so, we will use this:

$\tan^{-1}\frac{x}{2}+\tan^{-1}\frac{x}{3}=\tan^{-1}(\frac{\frac{x}{2}+\frac{x}{3}}{1-\frac{x}{2}\times \frac{x}{3}})=\frac{5}{4}\\\\\frac{5x}{6-x^2}=\tan \frac{5}{4}=0.021\\\\5x=0.021(6-x^2)\\\\5x=0.13-0.021x^2\\\\0.021x^2+5x-0.13=0$

By using quadratic formula, we can get that,

$x=-238.1,x=0.0259$

Ignoring negative value, the value of x = 0.0259.

Hence, the value of x = 0.0259.

Answer 2

"Formula: tan inverse of x + tan inverse of y is equal to tan inverse of x+ y upon 1- xy

According to this formula,

Tan inverse x upon 2 + tan inverse x upon 3 is equal to 5 by 4

Tan inverse of $\frac { x }{ 2 } +\frac { x }{ 3 } upon 1-{ x }^{ 2 }$by 6 is equal to 5 by 4

Tan inverse of 5x by 6 upon $6-{ x }^{ 2 }$by 6 is equal to 5 by 4

Tan inverse of 5x upon $6-{ x }^{ 2 }$ is equal to 5 by 4

5x upon $6-{ x }^{ 2 }$ is equal to tan of 5 by 4

By solving this we x = 0.0259"