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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!: 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(1744) About Me  (Show Source):
You can put this solution on YOUR website!
Remember your trig definitions,
sec(A)=1/cos(A)
tan(A)=sin(A)/cos(A)
Substitute
4*sec^2(A)-7*tan^2(A)=4/cos^2(A)-7*sin^2(A)/cos^2(A)
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(4-7*sin^2(A))
Remember also,
sin^2(A)+cos^2(A)=1
7*sin^2(A)+7*cos^2(A)=7
7*sin^2(A)=7-7*cos^2(A)
Substitute
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(4-7*sin^2(A))
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(4-(7-7*cos^2(A)))
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(4-7+7*cos^2(A)))
4*sec^2(A)-78tan^2(A)=(1/cos^2(A))(7*cos^2(A)-3))
Again,
sin^2(A)+cos^2(A)=1
3*sin^2(A)+3*cos^2(A)=3
Substitute again,
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(7*cos^2(A)-3)
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(7*cos^2(A)-(3*sin^2(A)+3*cos^2(A)))
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(7*cos^2(A)-3*sin^2(A)-3*cos^2(A))
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(4*cos^2(A)-3*sin^2(A))
This matches answer 1.
But that's not really in simplest terms,
4*sec^2(A)-7*tan^2(A)=(1/cos^2(A))(4*cos^2(A)-3*sin^2(A))
4*sec^2(A)-7*tan^2(A)=(4-(3*sin^2(A))/cos^2(A))
4*sec^2(A)-7*tan^2(A)=4-3*tan^2(A)