Question

Let tan(x)=2/5 . What is the value of tan(π+x) ?

Answer 1

`\boxed{\large{\bold{\blue{ANSWER~:) }}}}`

Here,

tan(x)=2/5

we have to find the value of tan(π+x)

we know that,

`\boxed{\sf{tan(A+B)=(tanA+tanB)/(1-tanA.tanB) } }`

According to the question,

`\sf{tan(π+x)=(tanπ+tanX)/(1-tanπ.tanX)}`

But,

• tanπ=0
• tanX=2/5

putting the value,

• 
  `\sf{tan(π+x)=(0+(2)/(5))/(1-0.(2)/(5))}`

• 
  `\sf{tan( π+x)=((2)/(5))/(1-0) }`

• 
  `\sf{tan( π+x)=((2)/(5))/(1) }`

• 
  `\sf{tan( π+x)=(2)/(5)×1 }`

• 
  `\sf{tan( π+x)=(2)/(5) }`

Therefore,

`\sf{The~ value~ of _{_(tan(π+x))}=(2)/(5) }`

Answer 2

tan (pi+x) = 2/5

Explanation:

Find tan (pi +x)

tan(A + B) = (tan A + tan B) / (1 − tan A tan B)

tan(pi + x) = (tan pi + tan x) / (1 − tan pi tan x)

tan(x)=2/5 and tan (pi) = 0

tan(pi + x) = (0 + 2/5) / (1 − 0*2/5)

= 2/5 /(1-0

=2/5