Simplify the expression (1-\frac{\cos61^\circ}{\cos1^\circ})(1-\frac{\cos62^\circ}{\cos2^\circ})\cdot...\cdot(1-\frac{\cos119^\circ}{\cos59^\circ})

pettingyg0

pettingyg0

Answered question

2022-04-25

Simplify the expression
(1cos61cos1)(1cos62cos2)(1cos119cos59)

Answer & Explanation

Zain Mccarty

Zain Mccarty

Beginner2022-04-26Added 15 answers

We have
i=159(1cos(60+i)cosi)=i=159cosicos(60+i)cosi
=i=1592sin(30+i)sin(30)cosi
=i=159sin(30+i}{cosi}
=i=159sin(90i)cosi
=i=1591=1

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