Question

Prove: (can only use left side to solve right side)
(sinx/1-cosx)+(1+cosx/sinx)=2(1+cosx)/sinx

Answer 1

take the LCM sinx(1-cosx)
and hopefully cancel values will be canceled out :)

Answer 2

well use a common denominator on the left side fractions

sin(x)(1 - cos(x))

so you have

\[\frac{\sin(x) \times \sin(x)}{\sin(x)(1 - \cos(x))} + \frac{(1 - \cos(x))(1 + \cos(x)}{\sin(x)(1 - \cos(x))}\]

simplify the fractions and write the numeratators over the common denominator

\[\frac{\sin^2(x) + 1 - \cos^2(x)}{\sin(x)(1 - \cos(x)}\]

Answer 3

so use the trig identity sin^2 = 1 - cos^2

so you have

\[\frac{\sin^2(x) + \sin^2(x)}{\sin(x)(1 - \cos(x))}\]

all you need to do is remove the common factor for the answer.

Answer 4

and you may need to check the right side is correctly written

Answer 5

yeah its correct you get the equation (2sin^2x)/sinx(1-cosx)
cancel the sinx and u get the right hand side

Answer 6

lol... my mistake with the numerator correct substitution, just wrong way around

use sin^2 = 1 - cos^2

so its

\[\frac{2(1 - \cos^2(x)}{\sin(x)(1 - \cos(x))}\]

factor the numerator, its the difference of 2 squares... then cancel the common factor

Answer 7

Thank you