JAMB - Mathematics (1987 - No. 30)
If tan \(\theta\) = \(\frac{m^2 - n^2}{2mn}\) find sec\(\theta\)
\(\frac{m^2 + n^2}{(m^2 - n^2)}\)
\(\frac{m^2 + n^2}{2mn}\)
\(\frac{mn}{2(m^2 + n^2)}\)
\(\frac{m^2n^2}{2(m^2 - n^2)}\)
Explanation
Tan \(\theta\) = \(\frac{m^2 - n^2}{2mn}\)
\(\frac{\text{Opp}}{\text{Adj}}\) by pathagoras theorem
= Hyp2 = Opp2 + Adj2
Hyp2 = (m2 - n2) + (2mn)2
Hyp2 = m4 - 2m2n4 - 4m2 - n2
Hyp2 = m4 + 2m2 + n2n
Hyp2 = (m2 - n2)2
Hyp2 = \(\frac{m^2 + n^2}{2mn}\)
\(\frac{\text{Opp}}{\text{Adj}}\) by pathagoras theorem
= Hyp2 = Opp2 + Adj2
Hyp2 = (m2 - n2) + (2mn)2
Hyp2 = m4 - 2m2n4 - 4m2 - n2
Hyp2 = m4 + 2m2 + n2n
Hyp2 = (m2 - n2)2
Hyp2 = \(\frac{m^2 + n^2}{2mn}\)
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