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91Ó°ÊÓ

find the exact value of the expression

cos-5Ï€4-cos3Ï€4

Short Answer

Expert verified

Value of the expression is 0

Step by step solution

01

Step 1. Given information

cos-5Ï€4-cos3Ï€4

02

Step 2. Rewriting the expression

As cos is a even function so, cos(x)=cos(-x)

So given expression can be written ascos5Ï€4-cos3Ï€4

03

Step 3. Calculations

Weknowthatcosπ+x=-cos(x)cosπ-x=-cos(x)So,cos(5π4)=cos(π+π4)=-cos(π4)cos(53π4)=cos(π-π4)=-cos(π4)So,cos(5π4)-cos(53π4)=0

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