Transform the expression from the left to the right.

Question

Tan A+ CotA to cscAsecA

Answer 1

So 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