How to simplify the expression (1+cosx)/sinx+sinx/(1+cosx)?

gibbokf5

gibbokf5

Answered question

2022-12-30

How to simplify the expression 1+cosxsinx+sinx1+cosx?

Answer & Explanation

Larry Newman

Larry Newman

Beginner2022-12-31Added 7 answers

Put on a common denominator first.
(1+cosx)(1+cosx)(sinx)(1+cosx)+sinx(sinx)(sinx)(1+cosx)
cos2x+2cosx+1+sin2xsinx(1+cosx)
Apply the pythagorean identity cos2x+sin2x=1:
1+2cosx+1sinx(1+cosx)
2+2cosxsinx(1+cosx)
Factor out a 2 in the numerator.
2(1+cosx)sinx(1+cosx)
2sinx
Finally, apply the reciprocal identity 1sinθ=cscθ to get:
2cscx

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