Question

Prove that (tanX + sinX)(1-cosX) = sin^2XtanX

Answer 1

expand the left hand side, what do you have?

Answer 2

tanX - tanXcosX + sinX - sinXcosX

Answer 3

tanx cos x = sinx ,so it cancel out with + sin x ,right?
so far, we have tan x - sinx cosx

Answer 4

Yes

Answer 5

hey, recheck the right hand side, is it right? is it \(sin^2 x tanx\)

Answer 6

Yes that's correct

Answer 7

ok, let me try, hehehe. I jump into the problem, not sure I can get the answer or not,

Answer 8

Haha okay thank you

Answer 9

ok, factor tan out

Answer 10

you get the answer, hehehe... I am lucky. !!!

Answer 11

Sorry to interrupt, but the left side can't be sin^2XtanX...
It's supposed to be sin^3XtanX...

Answer 12

the second term is sinx cosx = \(\dfrac{sinx cos x*cosx}{cosx}= tan x cos^2x\)

Answer 13

The left side is not sin^2XtanX, the right side is. @Loser66, what do you mean factor tan out?

Answer 14

now back to it tan x - tanx cos^2 x= tan x(1-sin^2x) = tan x sin^2x , oh yea!! this is right

Answer 15

I think I am lost...

Answer 16

ok, we have tanx - sinx cosx, right?

Answer 17

alternative :
see that :
tan(x) + sin(x) = tan(x) (1 + cos(x))

so,
(tanX + sinX)(1-cosX)
= tan(x) (1 + cos(x)) (1-cos(x))
= tan(x) (1 - cos^2(x))
= tan(x) sin^2 (x)