Question

1+sec2A/tan2A=cotA
prove that

Answer 1

(1+sec2A)/(tan2A)
= (1/tan2A) + (sec2A/tan2A)
= cot2A + csc2A
= [(cot^2 (A) - 1) / 2cotA] + [(1+tan^2 (A)) / 2tanA]
= [tanA (cot^2 (A) - 1) + cotA (1+tan^2 (A))] / (2 tanA cotA)
= [cotA - tanA + cotA + tanA] / 2
= 2 cotA / 2
= cotA.....hope this helps u..