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July 24, 2014

July 24, 2014

Posted by **Anonymous** on Sunday, October 27, 2013 at 3:28pm.

Tan A+ CotA to cscAsecA

- Pre-Calculus -
**Jai**, Sunday, October 27, 2013 at 4:30pmSo we must transform tan(A) + cot(A) into csc(A)*sec(A).

tan(A) + cot(A)

Note that cot(A) is equal to 1/tan(A). Substituting,

= tan(A) + 1/tan(A)

= (tan^2 (A) + 1) / tan(A)

Recall the pythagorean identity: tan^2 (A) + 1 = sec^2 (A). Also tan(A) = sin(A)/cos(A) and sec(A) = 1/cos(A). Substituting,

= sec^2 (A) / tan(A)

= sec^2 (A) * cos(A) / sin(A)

= sec(A) / sin(A)

Finally, 1/sin(A) = csc(A). Thus,

= sec(A) * csc(A)

Hope this helps~ :3

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