How do you simplify csc x(sin x + cos x)cscx(sinx+cosx)?

1 Answer
Lotusbluete
Feb 12, 2016

1 + cot x1+cotx

Explanation:

Knowing the two identities

csc x = 1 / sin x " "cscx=1sinx and " "cot x = cos x / sin x cotx=cosxsinx,

you can simplify as follows:

csc x (sin x + cos x ) = 1/ sin x (sin x + cos x)cscx(sinx+cosx)=1sinx(sinx+cosx)

= sin x / sin x + cos x / sin x =sinxsinx+cosxsinx

= 1 + cos x / sin x =1+cosxsinx

= 1 + cot x =1+cotx

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