simplify (cosx/1+sinx)+(1+sinx/cosx)

DofotheroU

DofotheroU

Answered question

2020-12-28

simplify (cosx/1+sinx)+(1+sinx/cosx)

Answer & Explanation

Faiza Fuller

Faiza Fuller

Skilled2020-12-29Added 108 answers

(cosx/1+sinx)+(1+sinx/cosx)=(cosx/1+sinx)+((cosx+sinx)/cosx)
=(cos2x+(1+sinx)(cosx+sinx))/cosx(1+sinx)
=(cos2x+cosx+sinx+sinxcosx+sin2x)/cosx(1+sinx)
=(1+cosx+sinx+sinxcosx)/cosx(1+sinx)
=(1+cosx+sinx(1+cosx))/cosx(1+sinx)
=(1+cosx)(1+sinx)/cosx(1+sinx)
=(1+cosx)/cosx
=1+secx

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