How do I solve sec(3x)-sqrt2 = 0 algebraically?

1 Answer
Apr 28, 2018

x= pi/12+2/3pin
x= (7pi)/2+2/3pin
n is an element of all integers

Explanation:

Let u be 3x:
sec(u)-sqrt2=0

secu= sqrt2

Apply reciprocal identity:
1/cosu= sqrt2

cosu= 1/sqrt2= sqrt2/2

u= pi/4 +2pin
u= (7pi)/4+2pin

Now replace u with 3x and solve for x:

3x=pi/4 +2pin
3x=(7pi)/4+2pin

x= pi/12+2/3pin
x= (7pi)/2+2/3pin

Here's a graph:
graph{sec(3x)-sqrt2 [-10, 10, -5, 5]}