prove the following identities
1.sin^4 A - cos^4 A =sin^2 A- cos^2 A
2.tan^2 A + (1/tan^2A)= (1/sin^2Acos^2A)-2
3.((1/cosA)-cosA)/((1/sinA)-sinA)=tan^3A
give me the steps plz
trigonometric relations
2009-05-11 3:26 am
回答 (2)
2009-05-11 3:45 am
2009-05-11 3:51 am
1.
L.H.S.=sin4A - cos4A
=(sin2A-cos2A)(sin2A+cos2A)
=sin2A-cos2A
=R.H.S.
2.
L.H.S.=tan2A + (1/tan2A)
= tan2A+cot2A
=(sec2A-1)+(csc2A-1)
=(sec2A+csc2A)-2
=(1/cos2A + 1/sin2A)-2
=(sin2A+cos2A)/(sin2Acos2A)-2
=(1/sin2Acos2A)-2
=R.H.S.
3.
L.H.S.=((1/cosA)-cosA)/((1/sinA)-sinA)
=[(1-cos2A)/cosA]/[(1-sin2A)/sinA]
=(sin2A/cosA)/(cos2A/sinA)
=sin3A/cos3A
=tan3A
=R.H.S.
2009-05-10 19:52:09 補充：
慢了...001最佳
L.H.S.=sin4A - cos4A
=(sin2A-cos2A)(sin2A+cos2A)
=sin2A-cos2A
=R.H.S.
2.
L.H.S.=tan2A + (1/tan2A)
= tan2A+cot2A
=(sec2A-1)+(csc2A-1)
=(sec2A+csc2A)-2
=(1/cos2A + 1/sin2A)-2
=(sin2A+cos2A)/(sin2Acos2A)-2
=(1/sin2Acos2A)-2
=R.H.S.
3.
L.H.S.=((1/cosA)-cosA)/((1/sinA)-sinA)
=[(1-cos2A)/cosA]/[(1-sin2A)/sinA]
=(sin2A/cosA)/(cos2A/sinA)
=sin3A/cos3A
=tan3A
=R.H.S.
2009-05-10 19:52:09 補充：
慢了...001最佳
收錄日期: 2021-04-22 00:38:52
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