Answer:

Step-by-step explanation (using the Unit Circle):
csc
- cos

csc =

sin
=

→ csc
=
=

cos
=

csc
- cos
=
-
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=
-
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=
-
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=
Step-by-step explanation (using the special triangles):
= 45°
a 45°-45°-90° triangle has sides with proportions of: 1 - 1 - √2
csc =
=

= 30°
a 30°-60°-90° triangle has sides with proportions of: 1 - √3 - 2
cos =
=
csc
- cos
=

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Answer: secθ
Explanation:
cosθ csc²θ tan²θ
= cosθ *
*
=
= secθ