+318 Verify the identity= (cos x/2-sin x/2)^2=1-sin x
can someone show work using the reciprocal identies.....struggling :(
+128406 (cos x/2-sin x/2)^2 = 1-sin x
Work with the left side
[ cos (x/2) - sin (x/2)] ^2 =
{cos (x/2) - sin(x/2) ] * [ cos(x/2) - sin (x/2) ] =
cos^2 (x/2) - 2sin(x/2)cos(x/2) + sin^2 (x/2)
Let x/2 = θ ......and we have that
cos^2 (θ) - 2sin(θ)cos(θ) + sin^2(θ) =
sin^2(θ) + cos^2(θ) - 2sin(θ)cos(θ) =
1 - sin (2θ) .....now.....back-substitute
1 - sin [ 2 (x/2) ] =
1 - sin x which = the right side !!!
