How do you use the fundamental identities to simplify $cot θ sec θ$ $cotthetasectheta$ ?

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Answer 1 · 2017-03-30T05:38:32

$csc θ$ $csctheta$

Identities to know:
$cot θ = \frac{cos θ}{cos θ}$ $cottheta=costheta/costheta$

$sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$

$csc θ = \frac{1}{sin θ}$ $csctheta=1/sintheta$

$cot θ sec θ = \frac{cos θ}{sin θ} \frac{1}{cos θ} = \frac{1}{sin θ} = csc θ$ $cotthetasectheta=costheta/sintheta1/costheta=1/sintheta=csctheta$

Answer 2 · 2017-03-30T05:42:45

$cot θ sec θ = csc θ$ $cotthetasectheta=csctheta$

As $cot θ = cos t h e \frac{a}{sin θ}$ $cottheta=costhea/sintheta$ and $sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$

$cot θ sec θ = \frac{cos θ}{sin θ} \times \frac{1}{cos θ}$ $cotthetasectheta=costheta/sinthetaxx1/costheta$

$=cancelcostheta/sinthetaxx1/cancelcostheta$

= $1/sintheta$

= $csctheta$

How do you use the fundamental identities to simplify cotthetasecthetacotθsecθcotthetasectheta?