Question

y = 3 . cossec x - sec x / tg x + 3 . cotg x

Answer 1

Dados: senx = 3/5

sen²x+cos²x=1

(3/5)²+cos²x=1

9/25+cos²x=1

cos²x = 1-9/25

cos²x = 16/25

cosx = +/- √(16/25)

cosx = +/-  4/5

Como "X" está no 1 quadrante.

Cosx  = + 4/5
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Y = 3.cossecx -secx/tgx + 3.cotgx

Y = 3*(1/senx) - (1/cosx)/(senx/cosx) +3.(cosx/senx)

Y = 3/senx - senx/cos²x +3cosx/senx

Y = 3/(3/5) - (3/5)/(4/5)²+3.(4/5)/(3/5)

Y = 3.(5/3) - (3/5)/(16/25)+ (4/5)*(5/3)

Y = 15/3 - (3/5)*(25/16) + (4*5)/(5*3)

Y = 5 - (3*25)*(5*16) + 20/15

Y = 5 -75/80 + 4/3

Y = 5 - 15/16 +4/3

mmc = 48

Y = (5*48-15*3+4*16)/48

Y = (240-45+48)/48

Y = 243/48

Y = 81/16