Question

wiedząc że tg alfa = 2/13 oblicz wartość wyrażenia tg alfa - cos alfa / sin alfa + cos alfa

Answer 1

tg alfa = 2/13 

zatem

y/x = 2/13

y = 2, x = 13

czyli 

r^2 = x^2 + y^2 = 13^2 + 2^2 = 169 + 4 = 173

r = p(173)

cos alfa = x/r = 13/p(173)

oraz

sin alfa = y/r = 2 / p(173)

Mamy więc

( tg alfa - cos alfa) / ( sin alfa + cos alfa) =

= ( 2/13 - 13/p(173))/ ( 2/ p(173) + 13/ p(173)) =

= ( 2/13 - 13/ p(173))/( 15/ p(173) ) =

= ( 2/13 - 13/ p(173) ) * ( p(173)/15) =

= ( 2 p(173))/195 - 13/15 = ( 2 p(173))/195 - 169/195 =

= ( 2 p(173) - 169)/195

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