Solve and prove the identity
(tan x+ cot (-x))/ (tan x - cot(-x))= 1-2cos^2(x)
2 answers
recall that cot -x = -cotx = -1/tanx
(sin/cos + cos-/sin-)/[sin/cos-cos-/sin-]
sin -x = -sin x
cos -x = cos x
(sin/cos - cos/sin)/[sin/cos+cos/sin]
multiply top and bottom by sin cos
(sin^2 - cos^2)/(sin^2 +cos^2)
but sin^2+cos^2 = 1
sin^2-cos^2
but sin^2=1-cos^2
1 - cos^2 -cos^2
1 - 2 cos^2
well, that is what is on the right :)
sin -x = -sin x
cos -x = cos x
(sin/cos - cos/sin)/[sin/cos+cos/sin]
multiply top and bottom by sin cos
(sin^2 - cos^2)/(sin^2 +cos^2)
but sin^2+cos^2 = 1
sin^2-cos^2
but sin^2=1-cos^2
1 - cos^2 -cos^2
1 - 2 cos^2
well, that is what is on the right :)
1 answer