Let t = tan@
(a) Express sin2@ and cos2@ in terms of t
(b) Hence, prove that
(sin2@ + 1) / ( 1 + cos2@ + sin2@) = (tan@ + 1) / 2
F4 Trigo Question
2009-02-05 3:22 am
回答 (2)
2009-02-05 3:26 am
✔ 最佳答案
Let t=tanxsin2x
=2sinxcosx
=2t/(1+t^2)
cos2x
=cos^2x-sin^2x
=(1-t^2)/(1+t^2)
(b)
(sin2x + 1) / ( 1 + cos2x + sin2x)
=(2t+1+t^2)/(1+t^2+1-t^2+2t)
=(t+1)^2/(2t+2)
=(t+1)/2
=(tanx+1)/2
2009-02-05 10:25 pm
Supplementary information:
Let t = tan@,
sin@ = t / (1 + t^2)^(1/2)
cos@ = 1 / (1 + t^2)^(1/2)
Let t = tan@,
sin@ = t / (1 + t^2)^(1/2)
cos@ = 1 / (1 + t^2)^(1/2)
收錄日期: 2021-04-26 13:04:28
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