a) Chứng minh rằng 1 + tan^2x = 1/cos^2x
VT =1 + sin^2 x /cos^2 x =(cos^2 x +sin^2 x) /cos^2 x
(cos^2 x +sin^2 x) =1 => (cos^2 x +sin^2 x) /cos^2 x =1/cos^2 x =VP =>dpcm

b) 1 + cot ^2x = 1/ sin^2x
VT =1 + cos^2 x /sin^2 x =(sin^2 x +cos^2 x) / sin^2 x
( sin^2 x +cos^2 x ) =1 => (cos^2 x +sin^2 x) /sin^2 x =1/ sin ^2 x =VP =>dpcm

c)
(1+cosx)/ sinx =sinx/(1-cosx)
<=> (1+cosx) (1-cosx) =sin^2 x
<=> (1-cos^2x) =sin^2 x
<=> 1 =cos^2x+sin^2 x luôn đúng => dpcm
d)
(tãnx +1)/(tãnx-1)=(1+cotx )/(1-cotx)
cơ bản tan x .cotx =1
VT = (1/cotx +1)/(1/cotx -1)=[(1+cotx ) /cotx ]/ [(1-cotx)/cotx]
=[(1+cotx ) ]/ [(1-cotx) ] =VP => DPCM
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e)
VT=(1-4sin^2 x cos^2 x )/(sinx -cosx )^2
=(1-(2sin xcos x)^2 )/(sinx -cosx )^2
=(1- sin^2 2x) /(sinx -cosx )^2
=(cos 2x) ^2 /(sinx -cosx )^2
=(cos^2x -sin^2 x) ^2 /(sinx -cosx )^2
=[(cos x -sin x)(cos x +sin x) ] ^2 /(sinx -cosx )^2
= (cos x -sin x)^2 (cos x +sin x)^2 /(sinx -cosx )^2
= (cos x +sin x)^2 =VP => dpcm
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