SOLUTION: Will someone please help me, I'm so confused! If we extablish an identity, (in simplest terms) 4 sec^2 A - 7 tan^2 A would equal what? 1. (4 cos^2 A - 3 sin^2 A)/(cos^2 A) 2. 4

Algebra ->  Trigonometry-basics -> SOLUTION: Will someone please help me, I'm so confused! If we extablish an identity, (in simplest terms) 4 sec^2 A - 7 tan^2 A would equal what? 1. (4 cos^2 A - 3 sin^2 A)/(cos^2 A) 2. 4       Log On


   

Question 150253: Will someone please help me, I'm so confused!
If we extablish an identity, (in simplest terms) 4 sec^2 A - 7 tan^2 A would equal what?
1. (4 cos^2 A - 3 sin^2 A)/(cos^2 A)
2. 4 - 3 tan^2 A
3. 1
4. (7 - 3 cos^2 A)/(cos^2 A)
Thank you so much for your time and help, Natalie!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Remember your trig definitions,
sec%28A%29=1%2Fcos%28A%29
tan%28A%29=sin%28A%29%2Fcos%28A%29
Substitute
4%2Asec%5E2%28A%29-7%2Atan%5E2%28A%29=4%2Fcos%5E2%28A%29-7%2Asin%5E2%28A%29%2Fcos%5E2%28A%29
4%2Asec%5E2%28A%29-7%2Atan%5E2%28A%29=%281%2Fcos%5E2%28A%29%29%284-7%2Asin%5E2%28A%29%29
Remember also,
sin%5E2%28A%29%2Bcos%5E2%28A%29=1
7%2Asin%5E2%28A%29%2B7%2Acos%5E2%28A%29=7
7%2Asin%5E2%28A%29=7-7%2Acos%5E2%28A%29
Substitute
4%2Asec%5E2%28A%29-7%2Atan%5E2%28A%29=%281%2Fcos%5E2%28A%29%29%284-7%2Asin%5E2%28A%29%29


4%2Asec%5E2%28A%29-78tan%5E2%28A%29=%281%2Fcos%5E2%28A%29%29%287%2Acos%5E2%28A%29-3%29%29
Again,
sin%5E2%28A%29%2Bcos%5E2%28A%29=1
3%2Asin%5E2%28A%29%2B3%2Acos%5E2%28A%29=3
Substitute again,
4%2Asec%5E2%28A%29-7%2Atan%5E2%28A%29=%281%2Fcos%5E2%28A%29%29%287%2Acos%5E2%28A%29-3%29



This matches answer 1.
But that's not really in simplest terms,

4%2Asec%5E2%28A%29-7%2Atan%5E2%28A%29=%284-%283%2Asin%5E2%28A%29%29%2Fcos%5E2%28A%29%29
4%2Asec%5E2%28A%29-7%2Atan%5E2%28A%29=4-3%2Atan%5E2%28A%29