How to prove the following: tan^2x+1+tanx secx = 1+sin x/ cos^2x

Cem Hayes 2021-03-02 Answered
How to prove the following:
tan2x+1+tanxsecx=1+sinxcos2x
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hosentak
Answered 2021-03-03 Author has 100 answers
tanxsecx=sinxcos2xorsinxsec2x.tan2x+1=sec2x.
So we have sec2x+sec2xsinx=sec2x(1+sinx)=1+sinxcos2x.
(To prove sec2x=tan2x+1, start with sin2x+cos2x=1, then divide through by cos2x:tan2x+1=sec2x because secx is 1cosx.)
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