- #1

Priyadarshi Raj

- 8

- 1

## Homework Statement

__Question:__Sum of all the solutions of the equation: ##tan^2 (33x) = cos(2x)-1## which lie in the interval ## [0, 314] ## is:

(a) 5050 π

(b) 4950 π

(c) 5151 π

(d) none of these

The correct answer is:

**(b) 4950 π**

## Homework Equations

## cos(2x) = 2cos^2(x) -1 ##

## The Attempt at a Solution

##tan^2 (33x) = cos(2x)-1##

⇒ ##tan^2 (33x) = 2cos^2(x)-2##

⇒ ##\frac{sin^2 (33x)}{cos^2(33x)} = 2(cos^2 (x) -1)##

⇒ ##sin^2 (33x) = 2cos^2(x)cos^2(33x) - 2cos^2 (33x)##

⇒ ##1 - cos^2(33x)= 2cos^2(x)cos^2(33x) - 2cos^2 (33x)##

⇒ ##2cos^2(x)cos^2(33x) - cos^2 (33x) - 1 = 0##

And I end up making it more complex. It'b be great if I could convert the ##33x## to something smaller.

Please help.