Question

I need to know how to simplify (sin(x)/(1-cos(x)))+((1-cos(x))/sin(x)) please include steps

Answer 1

\(\huge \frac{sinx}{1-cosx} + \frac{1-cosx}{sinx} \) this the problem?

Answer 2

Just take the LCM of the denominator and proceed further....You have to use (sinx)^2 + (cosx)^2 = 1 in a step

Answer 3

\(\large =\frac{sinx}{1-cosx} \cdot \frac{sinx}{sinx} + \frac{1-cosx}{sinx}\cdot \frac{1-cosx}{1-cosx} \)
\(\large = \frac{sin^2x +(1-cosx)^2}{(1-cosx)(sinx)} \)
\(\large = \frac{sin^2x +(1-2cosx+cos^2x)}{(1-cosx)(sinx)} \)
\(\large = \frac{2-2cosx}{(1-cosx)(sinx)} \)

can you take it from here? HINT: factor the numerator....

Answer 4

Thanks dpal and yes i can take it from there, i kept multiplying wrong on the lcm

Answer 5

yw...:)