Question

Verify the trigonometric identity: tan(2π - x) = tan(-x)

Answer 1

`\boxed{ \sf {view \: explanation}}`

Explanation:

`\Rightarrow \sf tan ( 2\pi - x)=tan(-x)`

`\sf Apply \ distributive \ law.`

`\Rightarrow \sf tan (2\pi) + tan (-x) =tan(-x)`

`\sf Apply : tan(2\pi) =0`

`\Rightarrow \sf 0 + tan (-x) =tan(-x)`

`\Rightarrow \sf tan (-x) =tan(-x)`

`\sf Hence \ verified.`

Answer 2

See Below

Explanation:

Taking Right Hand Side to verify the identity:

tan ( 2π - x)

Resolving Parenthesis

tan 2π + tan (-x)

We know that tan 2π = 0

0 + tan (-x)

=> tan(-x) = Left Hand Side

Hence Proved