0

Guest

Courses New

Simplify cos(a)cos(2a)cos(3a)...cos(999a) if a=(2pi)/1999

Simplify cos(a)cos(2a)cos(3a)...cos(999a) if a=(2pi)/1999

Grade:11

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
7 years ago
multiply divide by 2 sina in numerator nd denomenator
so you will get


\frac{1}{2^{999}} \frac{sin (2*999)a}{sin a}

\frac{1}{2^{999}} \frac{sin (1998)a}{sin a}
\frac{1}{2^{999}} \frac{sin (1999a - a)}{sin a}
\frac{1}{2^{999}} \frac{sin (2 pi - a)}{sin a}
-\frac{1}{2^{999}}
Piyush
15 Points
5 years ago
Let P=cosa cos2a cos3a.......cos999a 
Let Q=sina sin2a sin3a............sin999a
Now,
PQ×2^999=(2sinacosa)(2sin2acos2a)….......(2sin999acos999a)
=sin2a sin4a sin6a........sin1998a
=(sin2a sin4a....sin1998a){-sin(2π-100a)}{-sin(2π-1002a)}......{-sin(2π-1988a)}
=sin2a sin4a....sin998a sin999asin997a....sinx 
=Q
Hence P=1/2^999
 

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More