How do you use the fundamental identities to simplify $sin θ sec θ + cos θ csc θ$ $sinthetasectheta+costhetacsctheta$ ?

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Answer 1 · 2017-01-07T22:45:16

$\frac{1}{cos θ sin θ}$ $1/(costhetasintheta)$

Since

$sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$ and $csc θ = \frac{1}{sin θ}$ $csctheta=1/sintheta$

you get

$\frac{sin θ}{cos θ} + \frac{cos θ}{sin θ}$ $sintheta/costheta+costheta/sintheta$

$= \frac{{sin}^{2} θ + {cos}^{2} θ}{cos θ sin θ}$ $=(sin^2theta+cos^2theta)/(costhetasintheta)$

$= \frac{1}{cos θ sin θ}$ $=1/(costhetasintheta)$

How do you use the fundamental identities to simplify sinθsecθ+cosθcscθsinthetasectheta+costhetacsctheta?