Question

prove that tan(180-theta) = -tan theta​

Answer 1

Step-by-step explanation:

Take theta equal to alpha

$tan( \alpha - \beta ) = \frac{tan( \alpha ) - tan( \beta )}{1 + tan \alpha tan \beta }$

Putting values

$\tan(180 - \alpha ) = \frac{ \tan(180 ) - \tan( \alpha ) }{1 + \tan(180) \tan( \alpha ) }$

Tan 180 = 0

Put values

We get

- tan (theta or alpha)

Answer 2

Step-by-step explanation:

Take theta equal to alpha

tan( \alpha - \beta ) = \frac{tan( \alpha ) - tan( \beta )}{1 + tan \alpha tan \beta }tan(α−β)=

1+tanαtanβ

tan(α)−tan(β)

Putting values

\tan(180 - \alpha ) = \frac{ \tan(180 ) - \tan( \alpha ) }{1 + \tan(180) \tan( \alpha ) }tan(180−α)=

1+tan(180)tan(α)

tan(180)−tan(α)

Tan 180 = 0

Put values

We get