We want to divide by secΘ, which we can do unless secΘ=0. But secant is always either >1 or < -1, so it's okay to divide by it. Thus:
secΘ=1, meaning 1/cosθ=1
But then cosθ=1 too.
So we want the point(s) where secΘ=1, which are also where cosΘ=1. The only such point from 0≤Θ<360 is Θ=0 degrees.
Please do not trust the other user below, who tells us that we want cosΘ = 0. If cosΘ=0, then secΘ is not defined and the equation is not valid. Thus he has my solution (Θ=0) and two solutions that are invalid.
You see, in his algebra, he goes from:
1/cos²Θ = 1/cosΘ
to:
cos²Θ = cosθ
However, that step involves multiplying both sides by cosΘ. If cosΘ=0, then he just multiplied both sides by zero, not to mention he would initially have:
1/0 = 1/0
Neither quantity is defined, and thus cosΘ=0 is definitely not allowed.
This answer is fake. in any different case, the two the equation is written incorrectly in any different case there is extra techniques in the priority that wasn't secure in the define you wrote. Double verify which you typed the priority wisely and which you secure each and all of the techniques that became given in the priority.
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Verified answer
tan² θ + 1 = sec² θ
sec ² θ = sec θ
1 / cos ² θ = 1 / cos θ
cos θ = cos ² θ
cos ² θ - cos θ = 0
cos θ (cos θ - 1) = 0
cos θ = 0 , cos θ = 1
θ = 90° , 270° , 0°
tan²Θ +1 = secΘ
sec²Θ = secΘ
We want to divide by secΘ, which we can do unless secΘ=0. But secant is always either >1 or < -1, so it's okay to divide by it. Thus:
secΘ=1, meaning 1/cosθ=1
But then cosθ=1 too.
So we want the point(s) where secΘ=1, which are also where cosΘ=1. The only such point from 0≤Θ<360 is Θ=0 degrees.
Please do not trust the other user below, who tells us that we want cosΘ = 0. If cosΘ=0, then secΘ is not defined and the equation is not valid. Thus he has my solution (Θ=0) and two solutions that are invalid.
You see, in his algebra, he goes from:
1/cos²Θ = 1/cosΘ
to:
cos²Θ = cosθ
However, that step involves multiplying both sides by cosΘ. If cosΘ=0, then he just multiplied both sides by zero, not to mention he would initially have:
1/0 = 1/0
Neither quantity is defined, and thus cosΘ=0 is definitely not allowed.
This answer is fake. in any different case, the two the equation is written incorrectly in any different case there is extra techniques in the priority that wasn't secure in the define you wrote. Double verify which you typed the priority wisely and which you secure each and all of the techniques that became given in the priority.