Question

if sec A = 5/4 verify that tanA/1+tan^2A= sinA/secA

Answer 1

sec A =5/4
By pytagorous theorem other side is 3
now
tanA/1+tan^2A
3/4
------
1+9/16

3/4
------
25/16

3/4×16/25
12/25. ------(1)

now sinA/secA
3/5
------
5/4
3/5×4/5
.
12/25. -----(2)

hence from 1 and 2 LHS = RHS