Question

tanx sinx tanx - sinx
-------- = -----------
tanx + sinx tanx - sinx

prove each identity
i got the answer just wanna double check it

Answer 1

are u sure abt the denominator of RHS?

Answer 2

my bad
its:

tanx sinx tanx - sinx
-------- = -----------
tanx + sinx tanx sinx

imma lil sleepy rii now
could explain -.-

Answer 3

tan^2 x sin^2 x= tan^2x (1-cos^2 x)=tan^2 x- sin^2 x
now, factorise and rearrange

Answer 4

lol ok
on the LHS multiply top and bottom by cos x
\[\frac{(tanxsinx)cosx}{(tanx+sinx)cosx}\]\[=\frac{sinx \times sinx}{sinx+sinxcosx}\]\[=\frac{\sin^2x}{sinx+sinxcosx}\]\[=\frac{1-\cos^2x}{sinx(1+cosx)}\]\[=\frac{(1-cosx) \cancel{(1+cosx)}}{sinx \cancel{(1+cosx)}}\]\[=\frac{1-cosx}{sinx}\]now multiply top and bottom by tanx\[=\frac{tanx-sinx}{sinxtanx}\]

Answer 5

Thaaankksss Guyss <3
i know i sound so gay right noww.....lol

Answer 6

lool ur welcome