Question

tan⁻¹2x+tan⁻¹(1/x+4)= π/2,Solve it.

Answer 1

Answer:

........... ............

Answer 2

Answer:

x=0

Step-by-step explanation:

according to formula,

tan⁻¹a + tan⁻¹b=  tan⁻¹($\dfrac{a+b}{1-ab}$)

let's consider a= 2x and b=1/x+4

now,

=> tan⁻¹2x+tan⁻¹(1/x+4)=$\dfrac{\pi }{2}$

=>  tan⁻¹($\dfrac{2x+1/x+4}{1-(2x)(1/x+4)}$) = $\dfrac{\pi }{2}$

=> ($\dfrac{2x+1/x+4}{1-(2x)(1/x+4)}$) = tan $\dfrac{\pi }{2}$

=>$\dfrac{2x^{2} +4x+1 }{-7x} =\infty$

=> -7x= 0

=> x=0