Evaluatecos(π-x)
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
Thus,cos(π-x) =-cosx