Can anyone help verify the problem: sin x - cosx/sinx + cos x - sin x/cos x = 2 - secx*cscx Thanks!?

Answer 1

(sin x - cos x) / sin x + (cos x - sin x) / cos x ( that' the right Q)
multiply first term by cos x and second term by sinx, you end up with as follows:
(sin x*cos x - cos^2x + cos x*sin x - sin^2 x) / sin x*cos x
(2sin x*cos x - (sin^2x + cos^2x)) / sin x*cos x
(2sin x*cos x / sinx*cos x) - (1 / sin x*cos x)
2 - sec x*csc x

Answer 2

Question should have brackets:-
LHS
(sin x - cos x) / sin x + (cos x - sin x) / cos x
Common denominator, D , is sin x.cosx
Numerator ,N,then becomes:-
cos x.(sin x - cos x) + sin x.(cos x - sin x)
2 sinx cos x - (cos²x + sin²x)
2 sin x.cos x - 1
Dividing N by D:-
N / D = (2 sin x.cos x - 1) / sinx.cos x
N / D = 2 - 1 / (sin x.cosx)
N / D = 2 - sec x.cosec x as required

Answer 3

It's true. I didn't verify it but who cares. Why don't you do your own homework instead of trusting random strangers on the internet for your grade?