Find sin 2x cos 2x and tan 2x from the given information tan

Find sin 2x, cos 2x, and tan 2x from the given information, tan x = 1/4 cos x > 0 Sin 2x = squareroot 17/17 cos 2x= tan 2x=

Solution

tanx = -1/4 cosx>0 --> sinx<0

sinx = -1/sqrt(17)

cosx = 4/sqrt(17)

a)sin2x = 2sinxcosx = -8/17

b)cos2x = 1-2sin^2x = 15/17

c)tan2x = sin2x/cos2x = -8/15