Simplify Sen(x) + Cos(x)Cot(x)?

sin(x) + cos(x)cot(x)

sin(x) + cos(x)[cos(x)/sin(x)]

sin(x) + cos²(x)/sin(x)

sin²(x)/sin(x) + cos²(x)/sin(x)

[sin²(x) + cos²(x)]/sin(x)

Since sin²(x) + cos²(x) = 1:

1/sin(x)

csc(x)

Cot X Cos X

sin x + cos x cot x = sin x + cos x • cos x/sin x = sin x + cos^2 x/sin x = (sin^2 x + cos^2 x)/sin x = 1/sin x = csc x

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1/sin - cos* (cos/sin) (1-cos²)/sin since sin² + cos² = 1 you can rearrange: sin² = 1 - cos² Therefore: sin²/sin Answer --> sin(x) Note: all the sine and cosine terms should have an x variable within them but i left them out to simplify notation. ie. sin = sin(x)

Sin(x) + Cos(x)Cot(x)

Cot(x) = Cos(x)/Sin(x)

Sin(x) + Cos(x)Cos(x)/sin(x)

Sin(x) +cos^2(X)/Sin(x)

(Sin^2(x) + cos^2(x))/Sin(x)

Sin^2(x) + cos^2(x)=1

=(Sin^2(x) + cos^2(x))/Sin(x)=

1/Sin(x) = cosec(x)

sinx+cosx * cosx/sinx

=sinx+cos^2x/sinx

=(sin^2x+cos^2x)/sinx

=1/sinx

=cscx

sinx + cos x ( cos x / sin x )

sin ² x + cos ² x

------------------------

sin x

1

-------

sin x

cosec x