What is $cottheta-csctheta-costheta$ in terms of $sintheta$ ?

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Answer 1 · 2015-12-09T01:05:13

$(costheta-costhetasintheta-1)/sintheta, theta!=0^@, 180^@, 360^@$

Recall:
$1. cotx=1/tanx$ or $cosx/sinx$
$2. cscx=1/sinx$

Substitute your reciprocal and quotient identities into the equation:

$cottheta-csctheta-costheta$

$=costheta/sintheta-1/sintheta-costheta$

$=(costheta-1-costheta(sintheta))/sintheta$

$=(costheta-1-costhetasintheta)/sintheta$

$=(costheta-costhetasintheta-1)/sintheta, theta!=0^@, 180^@, 360^@$

What is cottheta-csctheta-costhetacottheta-csctheta-costheta in terms of sinthetasintheta?