Need to prove identity: cotA(secA-cosA)=sinA

[joanne1102]

Need to prove identity: cotA(secA-cosA)=sinA

I distributed cotA to arrive at: cotAsecA - cotAcosA. Then used quotient identity for cotA and reciprocal identity for secA. Can't get past that. What steps would be next or should I have started with different steps. Also supposed to justify each step. Any help is appreciated.

 

[stapel]

...Then used quotient identity for cotA and reciprocal identity for secA. Can't get past that....

Please reply showing these steps and your final result so far. Thank you!

Eliz.

 

[mathmathmath93]

cotA(secA-cosA)=sinA

I would change that to:
cos/sin ( 1/cos - cos) = sin
Distribute for:
1/sin - cos^2/sin = sin
change to:
(sin^2 + cos^2)/sin - cos^2/sin = sin
combine and subract for:
sin^2/sin = sin
-->
sin=sin

Hurrah.