Question

A+B+C=180 Sinc=1 then prove tanA.tanB=1
plz do it

Answer 1

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A+B+C=180

if ,
SinC=1
then C = 90°

then , A + B = 90°

Now.
$\\ \tan(A + B ) = \frac{ \tan(A ) + \tan(B) }{ 1 - \tan(A ) \tan( B ) } \\ \\ \tan( 90°) = \frac{ \tan(A ) + \tan(B) }{ 1 - \tan(A ) \tan( B ) } \\ \\ \frac{1}{0} = \frac{ \tan(A ) + \tan(B) }{ 1 - \tan(A ) \tan( B ) } \\ \\1 - \tan(A ) \tan( B ) \times (1) = \tan(A ) + \tan(B) \times (0) \\ \\ 1 - \tan(A ) \tan( B ) = 0 \\ \tan(A ) \tan( B ) = 1.....proved$
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