Identity Functions Detailed
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Prove the given identity - Please explain in detail.
14. 2 cos x - 2 cos^3x = sin x sin 2x
16. cos (x-y)/cos x cosy = 1 tan x tany
20. sec x -cos x = sin x tanx
22. sin 2x = 1/tanx +cot 2x
23. If tan x = 5/12 and sin x>0 , find sin 2x
26. If sin x = -12/13 with pie <x<3pie/2, and sec y = 13/12 with 3 pie/2 < y< 2 pie, find cos (x+y)
28. If sin x = -2/5 and 3pie/2 < x< 2 pie, then cos (pie/4+x) = ?
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The expert identifies trigonometric functions.
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14. 2 cos x - 2 cos^3x = sin x sin 2x
Proof: 2 cos x - 2 cos^3x =2cosx(1-cos^2x)=2cosxsin^2x=(2sinxcosx)sinx=sin2xsinx
Thus 2 cos x - 2 cos^3x =sinx sin2x
16. cos (x-y)/cos x cosy = 1+ tan x tany
Proof: cos (x-y)/cos x cosy=(cosxcosy+sinxsiny)/cosxcosy=1+sinxsiny/cosxcosy
=1+tanx tany
Thus cos (x-y)/cos x cosy=1+tanx ...
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