Sin+Cos/Sin - Cos-Sin/Cos = Sec x Csc?

Question

Using Trigonometric Identities.


help

Answer 1

Brackets required:-
LHS
(sin x + cos x) / sin x - (cos x - sin x) / cos x

Common denominator = sin x cos x

Top line
N = cos x (sin x + cos x) - sin x (cos x - sin x )

Bottom line
D = sin x cos x

N / D
(cos ² x + sin ² x) / sin x cos x
1 / (sin x) (cos x)
cosec x sec x

RHS
sec x cosec x

LHS = RHS

Answer 2

Hi,
Unfortunately, this is not true. As we know, Sec = 1/cos, and Csc = 1/sin
I tried to make expression as one with common denominator,
like this: (sin^2*cos + cos^2 - cos^2*sin - sin^2)/sin*cos, the expression would equal sec*csc in case the numerator of this fraction would equal to 1 identically.
I could not receive it.
So, let us find the opposite result. In case we have the angle 45 degrees, sin = cos , the left side identically equals zero, and the right side of the offered equation equals to 2.
So there is some mistake in conditions.
Sorry.

Answer 3

Looks like jibberish to me