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Use trigonometric identities to simplify the expression.

cot(β+π)sin(β

1 Answer

5 votes

Answer:

cosβ

Explanation:

cot(β+π)sinβ

cot(x)=cos(x)/sin(x), so we can rewrite our expression as:

(cos(β+π)/sin(β+π)) * sinβ

sin(a+b)=sin(a)cos(b)+cos(a)sin(b), so we can rewrite our expression as:

(cos(β+π)/(sinβcosπ+cosβsinπ)) * sin(β)

cos(a+b)=cos(a)cos(b)-sin(a)sin(b), so we can rewrite our expression as:

(cosβcosπ-sinβsinπ)/(sinβcosπ+cosβsinπ)) * sin(β)

cosπ=-1 and sinπ=0, so we can rewrite our expression as:

(-cosβ)/(-sinβ) * sin(β)

(-cosβ)/(-sinβ) * sin(β)

=(cosβ/sinβ)(sinβ)

=cosβ

User Ken Yeoh
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