Question

tan inverse 1+tan inverse x=0 then value of x is​

Answer 1

Answer:

${tan}^{ - 1} 1 + {tan}^{ - 1} x= 0 \\ \frac{\pi}{4} + {tan}^{ - 1}x = 0 \\ {tan}^{ - 1}x = - \frac{\pi}{4} \\ x = tan( - \frac{\pi}{4} ) \\ x = - tan \frac{\pi}{4} \\ x = - 1$

Answer 2

Value of x is  - 1 if tan⁻¹(1) + tan⁻¹(x) = 0

Given:

• tan⁻¹(1) + tan⁻¹(x) = 0

To Find:

• Value of x

Solution:

tan⁻¹(-a)   = -tan⁻¹(a)

tan⁻¹(1) + tan⁻¹(x) = 0

Step 1:

Transpose tan⁻¹(1)  on RHS

tan⁻¹(x) =  -tan⁻¹(1)

Step 2:

Use tan⁻¹(-a)   = -tan⁻¹(a)

tan⁻¹(x) =   tan⁻¹(-1)

Step 3:

Taking tan both side

x =  - 1

Value of x is  - 1