How to solve this trigonometric question?

Question

sin x = 3/5 and 0 <x<π/2, 

calculate tan (π/2+2x)

Answer 1

tan (pi/2+2x)= sin(pi/2+2x)/(cos(pi/2+2x))

= -cos 2x/sin 2x

sin x=3/5 cos x=(4/5)

cos 2x =cos^2x-sin^2 x= 16/25-9/25=7/25

sin 2x= 2 sin x cos x=2 *3/5*4/5=24/25

tan(pi/2+2x)=-7/25*25/24= -7/24

=-0.29167

I hope, this value is correct.

Answer 2

arcsin(3/5)≈ 0.643501108...

tan[π/2 + 2arcsin(3/5)]≈ -0.291666...