(1−sinβ)(1+cscβ)=cscβ−sinβ

babeeb0oL

babeeb0oL

Answered question

2021-02-09

To find the equation (1−sin⁡β)(1+csc⁡β)=csc⁡β−sin⁡β

Answer & Explanation

komunidadO

komunidadO

Skilled2021-02-10Added 86 answers

Work on the left side. Apply distributive property:

(1−sin⁡β)(1+csc⁡β)=1(1−sin⁡β)+csc⁡β(1−sin⁡β)

(1−sin⁡β)(1+csc⁡β)=1−sin⁡β+csc⁡β−sin⁡βcsc⁡β

Use the reciprocal identity for cosecant:

(1−sin⁡β)(1+csc⁡β)=1−sin⁡β+csc⁡β−sin⁡β×1sin⁡β

Simplify:

(1−sin⁡β)(1+csc⁡β)=1−sin⁡β+csc⁡β−1

(1−sin⁡β)(1+csc⁡β)=−sin⁡β+csc⁡β

or

(1−sin⁡β)(1+csc⁡β)=csc⁡β−sin⁡β

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