Please solve both questions Find sin2x cos2x and tan2x from

Please solve both questions

Find sin(2x), cos(2x), and tan(2x) from the given information.

tan(x) = 1/5 cos(x) > 0

sin2x

cos2x

tan2x

sin(x) = 24/25 ; 0<x<90

cosx = sqrt(1 - sin^2x) = sqrt( 1- (24/25)^2 ) = 7/25

a) Use double angle formula : cos2x = 1 -2sin^2x

So, cosx = 1 -2sin^2(x/2)

sin(x/2) = sqrt[( 1 - cosx)/2]

= sqrt( (1 -7/25)) = sqrt( 18/25) = 3sqrt(2)/5

b) cos(x/2):

Use double angle formula : cos2x = 2cos^2x -1

cos(x/2) = sqrt[ (1+cosx)/2]

= sqrt[ (1+7/25) ]

= sqrt[32/25]

= 4sqrt(2)/4

c) tan(x/2) = sin(x/2)/cos(x/2) = 3/4