Question

if A and B are two complementary angle s .Show that tanB + sinB=sinB/sinA*(1+cosB)​

Answer 1

Answer:

$= > \tan( \beta ) + \sin( \beta ) = \frac{ \sin( \beta ) }{ \sin( \alpha ) } \times (1 + \cos( \beta )) \\ = > \frac{ \sin( \beta ) }{ \cos( \beta ) } + \sin( \beta ) = \frac{ \sin( \beta ) }{ \sin( \frac{\pi}{2 } - \beta ) } \times (1 + \cos( \beta ) )\\ = > \sin( \beta ) \frac{ (1 + \cos( \beta ) )}{ \cos( \beta ) } = \frac{ \sin( \beta ) }{ \cos( \beta ) } \times (1 + \cos( \beta ) ) \\ = > \tan( \beta ) (1 + \cos( \beta )) = \tan( \beta ) (1 + \ \cos( \beta ) ) \\ hence \: \: \: \: proved$

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