Question

Given (1+cosx)/(sinx) + (sinx)/(1+cosx) =4, find a numerical value of one trigonometric function of x.

a. tanx=2
b. sinx=2
c. tanx=1/2
d. sinx=1/2

Answer 1

D

Explanation:

Edge2021

Answer 2

`sin(x)=(1)/(2)`

Explanation:

we are given

`(1+cos(x))/(sin(x))+(sin(x))/(1+cos(x)) =4`

We will make common denominator

`((1+cos(x))* (1+cos(x)))/((sin(x))* (1+cos(x)))+(sin(x)* sin(x))/((1+cos(x))* sin(x)) =4`

now, we can simplify it

`(1+cos^2(x)+2cos(x)+sin^2(x))/((sin(x))* (1+cos(x)))=4`

`(2+2cos(x))/((sin(x))* (1+cos(x)))=4`

`(2(1+cos(x)))/((sin(x))* (1+cos(x)))=4`

now, we can cancel it

`(2)/(sin(x))=4`

`(2)/(4)=sin(x)`

we can simplify it

and we get

`sin(x)=(1)/(2)`