Evaluate cos (pi-x)

Linda Horne

Linda Horne

Answered question

2023-03-24

Evaluate cos ( π x )

Answer & Explanation

chumanhonv19s

chumanhonv19s

Beginner2023-03-25Added 4 answers

We know that cos(A-B)=cosAcosB+sinAsinB
cos(π-x)=cosπcosx+sinπsinx
Solving cosπ,sinπusing supplementary angle concept of trigonometry, we get
cosπ=cos1800
=cos(900+900)
=-sin900
cosπ=-1 From Trigonometric Angle Table sin900=1
sinπ=sin1800
=sin(900+900)
=cos900
sinπ=0 From Trigonometric Angle Table cos900=0
cos(π-x)=(-1)×cosx+0×sinx From above cosπ=-1
=-cosx
Therefore,cos(π-x)=-cosx

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