If tan θ θ = m2−n22mn m 2 − n 2 2 m n find secθ

If tan $\theta$ = $\frac{m^2-n^2}{2mn}$ find sec$\theta$

Answer Details

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 = $\frac{m^2+n^2}{2mn}$