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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