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Chapter 7: Q. 80 (page 475)

Establish each identity.

sin胃+cos胃sin胃-cos胃-sin胃cos胃=sec胃csc胃

Short Answer

Expert verified

The left side of the given equation has been simplified to bring the right side.

Step by step solution

01

Step 1. Given Information

The given equation issin胃+cos胃sin胃-cos胃-sin胃cos胃=sec胃csc胃

02

Step 2. Calculation

Consider the left side of the given equation and simplify to bring the right side in order to establish the equation.

sin胃+cos胃sin胃-cos胃-sin胃cos胃=cos胃(sin胃+cos胃)-sin胃(cos胃-sin胃)sin胃cos胃=cos胃sin胃+cos2胃-sin胃cos胃+sin2胃sin胃cos胃=sin2胃cos2胃sin胃cos胃=1sin胃cos胃=sec胃csc胃

Hence, Proved

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