Question

If 4sin(x) = 3cos(x) Find :

$\frac{sec^{2}(x) }{4(1- tan^{2} )}$

Answer 1

4 sin(x) = 3 cos (x)
⇒sin(x)/cos(x) = 3/4
⇒tan(x) =3/4
⇒tan²x = 9/16
sec²(x) = 1+tan²x = 1+9/16 = 25/16
now putting the values
(25/16)/[4(1-9/16)]
=(25/16)/(7/4)
=25/28