To solve the the question we proceed as follows:
From trigonometric laws
(cos x)^2+(sin x)^2=1
(cos y)^2+(sin y)^2=1
sin (x-y)=sin x sin y-sin y cos x
cos (x-y)=cos x cos y+ sin x sin y
si x=8/17
cos x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(225/289)=15/17
cos y=3/5
sin x= sqrt(1- (cos x)^2)= sqrt(1-9/25)=sqrt(16/25)=4/5
thus
tan (x-y)=[sin (x-y)]/[cos (x-y)]
=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]
plugging in the values we obtain:
[8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]
simplifying
[24/85-60/85]/[45/85+32/85]
=-36/77
Answer:
x = 7
Step-by-step explanation:
Answer:
The number is 13.
Step-by-step explanation:
We are given the following in the question:
Let x be the variable, then according to the question
"The sum of eight and eleven times a number is 151"
We can write the equation:
Solving the equation, we can write:
Thus, the number is 13.