Question 150253
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)}}}