Trigo Problem

1) Please do this sum without using Complex no.(Actually this sum can be solved by pure trigonometry...)

1: if theta= pi/1999 then find the value of cos(theta) x cos(2theta) x cos(3theta) x ..... cos 999(theta)

2 Answers

just multiply and divide by 2 sinx initially then in every step multiply 2.
the answer will come out to be 12⁹⁹⁹.

btw, how would you do this by using complex numbers?

Actually by trigo i did this way:

Let x=cos(theta) x cos(2theta) x cos(3theta) x ...cos(999theta)

Let y= sin(theta) x sin(2theta) x sin(3theta) x .....sin(999theta)

now xy=cos(theta)sin(theta) x sin(2theta)cos(2theta) x ...cos(999theta)sin(999theta)

now 2⁹⁹⁹xy=sin(2theta) x ........sin(1998theta)

Now sin(1998theta)=sin(theta) n so on..

We get 2⁹⁹⁹xy=y

So x=1/2⁹⁹⁹.

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