Question

prove : tan 130-tan 90-tan 40=tan130tan90tan40

Answer 1

[0010001111]... Hello User... [1001010101]
Here's your answer...

The formula we'll be using here is...
$\tan( \alpha - \beta ) = \frac{ \tan( \alpha ) - \tan( \beta ) }{1 + \tan( \alpha ) \tan( \beta ) } \\ \tan( \alpha ) - \tan( \beta ) = \tan(\alpha - \beta ) (1 + \tan( \alpha ) \tan( \beta ) )$
Substituting alpha as 130° and beta as 40°...

$\tan130 - \tan40 = \tan(130 - 40) (1 + \tan130 \tan40 ) \\ \tan130 - \tan40 = \tan90 (1 + \tan130 \tan40 ) \\ \tan130 - \tan40 = \tan90 + \tan130 \tan90 \tan40 \\ \tan130 - \tan90 - \tan40 = \tan130\tan90 \tan40$
Hence Proved

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