trig help (1 Viewer)

[xXmuffin0manXx]

i) prove cosx-cos(x+2theta) all over 2sintheta = sin(x+theta)

ii) using 2cos^2 x = 1 +cos2x
prove 8cox^4 x=3+4cos2x+cos4x

thank you

 

[Timothy.Siu]

i) prove cosx-cos(x+2theta) all over 2sintheta = sin(x+theta)

hmm i sorta used differences of products which isn't really in the course...

LHS=(cos x-cos(x+2A))/2sin A x sin(x+A)/sin(x+A)
=sin(x+A) . (cos x-(cos (x+2A))/2sinAsin(x+A)
=sin(x+A) . (-2sin(x+A)sin(-2A))/2sinAsin(x+A)
=sin(x+A)=RHS

 

[Drongoski]

2nd one is fun!


8cos ⁴ x = 2 [ (2cos²)² ]

= 2 [ (1 + cos2x)² ]

= 2 [ (1 + 2 cos 2x + cos² 2x ) ]

= 2 + 4 cos 2x + 2 cos² 2x

= 2 + 4 cos 2x + 1 + cos 4x

= 3 + 4 cos 2x + cos 4x

= RHS


QED