So starting with LHS:eginalignfrac1sin x − sin x &= frac1 − (sin x)^2 sin x \ &= frac(cos x)^2 sin x endalign

I am grounding now and wanted to know how should ns proceed. Is this much correct?

Its done. Just split the molecule as:

$$ fraccos x . cos x sin x$$

$$= fraccos x sin x . cos x $$

$$= cot x . cos x $$

Proved!

I loved these in mine precalculus class. Let"s go.

You are watching: Csc x - sin x = cot x cos x

You"re right but went one too far. Write:

$$ fraccos^2 xsin x = cos x cdot fraccos xsin x $$

from whence the an outcome follows.

I"ll deal with it specifically

Yes, begin with LHS-$$cos,x−sin,x=(cot,x)(cos,x)$$$$cos,x−sin,x=dfrac1sin,x-sin,x;;;;;;;;;;;;;;;;;;\because cos,x=dfrac1sin,x$$$$=dfrac1-sin^2xsin,x$$$$=dfraccos^2xsin,x;;;;;;;;;;;;;;;;;;\because1-sin^2x=cos^2x$$Write $cos^2x$ as-

$cos,xcdot cos,x$$$dfraccos,xcdot cos,xsin,x=dfraccos,xsin,xcdot cos,x$$$$cot,xcdot cos,x;;;;;;;;;;;;;;;;;;;;;;\becausedfraccos,xsin,x=cot,x$$

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