Question

determine o valor de m na expressão: sendo sen x= 3/5
M= 3cossec x - sec x
______________
tg x+ 3 cotg x

Answer 1

M = (3.cossec x - sec x)/(tg x + 3.cotg x)

cossec x = 1/sen x

cossec x = 5/3

sen² x + cos² x = 1

(3/5)² + cos² x = 1

cos² x = 1 - 9/25

cos² x = 25/25 - 9/25

cos² x = 16/25

cos x = √(16/25)

cos x = 4/5

sec x = 1/cos x

sec x = 5/4

tg x = sen x/cos x

tg x = 3/5 ÷ 4/5

tg x = 15/20

tg x = 3/4

cotg x = cos x/sen x

cotg x = 4/5 ÷ 3/5

cotg x = 20/12

cotg x = 5/3

M = [3.(5/3) - 5/4 ] / [3/4 + 3.(5/3)]

M = [5 - 5/4] / [3/4 + 5]

M = [20/4 - 5/4] / [3/4 + 20/4]

M = 15/4 ÷ 23/4

M = 60/92

M = 15/23