Find a simplified form of the expression below:

Question

1-sin(x) cot(x) cos(-x)

please help me

Answer 1

1 - sin x (cos x / sin x) (cos -x)

1 - (cos x)(cos x)

1 - cos² x

sin² x

Answer 2

To simplify 1-sin(x)cot(x)cos(-x) you’ll need the following identities:

negative angle identity:

cos(-x)=cos(x)

Quotient identity:

cot(x)=cos(x)/sin(x)

Pythagorean identity:

sin²(x)=1-cos²(x)

1-sin(x)cot(x)cos(-x)

=1-sin(x)cot(x)cos(x). Negative angle identity

=1-sin(x)*{cos(x)/sin(x)}*cos(x). Quotient identity

=1-cos(x)cos(x). Cancel sin(x)

=1-cos²(x)

=sin²(x). Pythagorean identity.

Answer 3

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