Question

Cota + tana = x and seca - cosa = y, prove that (x^2y)^2/3 _ (xy^2)^2/3 =1

Answer 1

Answer:

i) cot A + tan A = {1 + tan^2 (A)}/tan A =

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

ii) sec A - cos A = {1 - cos^2 (A)}/cos A

= sin^2(A)/cos A = y

iii) So, x^2*y = {sec^4(A)/tan^2(A)}*{sin^2(A)/cos A}

= sec^3(A)

So (x^2*y)^(2/3) = {sec^3(A)}^(2/3) = sec^2(A)

Similarly 2nd term simplifies as: tan^2(A)

This left side = sec^2(A) - tan^2(A) = 1