help@askiitians.com

+91-93193 64476

Trigonometry> Simplify cos(a)cos(2a)cos(3a)...cos(999a)...

question mark

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

gdhh , 10 Years ago

Grade 11

2 Answers

Nishant Vora

multiply divide by 2 sina in numerator nd denomenator
so you will get

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

$\frac{1}{2^{999}} \frac{sin (1998)a}{sin a}$
$\frac{1}{2^{999}} \frac{sin (1999a - a)}{sin a}$
$\frac{1}{2^{999}} \frac{sin (2 pi - a)}{sin a}$
$-\frac{1}{2^{999}}$

Last Activity: 10 Years ago

Piyush

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

Last Activity: 7 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.

trigonometry

1 Answer Available

Last Activity: 3 Years ago

Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720

trigonometry

1 Answer Available

Last Activity: 4 Years ago

To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA

trigonometry

1 Answer Available

Last Activity: 4 Years ago

Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)

trigonometry

1 Answer Available

Last Activity: 4 Years ago

WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥

trigonometry

1 Answer Available

Last Activity: 4 Years ago

View all Questions